Optical properties and fabrication of dielectric metasurfaces based on amorphous silicon nanodisk arrays.

Dielectric metasurfaces based on amorphous silicon (a-Si) nanodisks are interesting for nanophotonic applications due to the high refractive index and mature/low temperature fabrication of a-Si. The investigated metasurfaces consist of a-Si nanodisk arrays embedded in a transparent film. The diameter-dependent optical properties of the nanodisk Mie resonators have been investigated by finite-difference time-domain (FDTD) simulations and spectrally-resolved reflectivity and transmission measurements. Well-ordered substrate-free a-Si nanodisk arrays were fabricated and characterized with regard to their broadband anti-reflection properties when placed on a crystalline silicon (c-Si) surface, and reflectivity/ transmission properties when embedded in a polydimethylsiloxane (PDMS) film. Our results confirm broadband anti-reflection when placed on silicon, while the optical characteristics of the nanodisks embedded in PDMS are shown to be potentially useful for color/NIR filter applications as well as for coloring on the micro/nanoscale.

High-index dielectric (e.g., semiconductor) nanostructures support geometrical (Mie-like) resonances in the visible-NIR spectral range, with scattering cross-sections larger than their geometrical cross-sections [2][3][4][5][6]. The Mie resonances in dielectric materials are formed by displacement currents instead of actual currents, resulting in lower losses than in metallic materials. Scattering of spherical particles in a homogeneous medium has been extensively studied in Mie theory [22] including analysis of particles weakly coupled to the substrate.
The optical antenna effect in dielectric nanostructures [1] has been utilized for broadband omnidirectional anti-reflection using etched c-Si nanodisk arrays on a c-Si substrate. Without coating an average surface reflection of ~7.5% was obtained in the spectral region of 450-900 nm [2]. An additional thin SiN-layer coating resulted in an average surface reflection even as low as ~1.3%. First and second order Mie resonances were identified, which are related to the geometrical properties of the Mie resonator. The presence of a sharp reflection dip (periodicity dip) is also reported and is due to the Wood-Rayleigh anomaly [23], related to the grating effect of the regular nanodisk array. A redshift of the Mie resonances is observed as the nanodisk diameter increases, indicating that specific resonance wavelengths can be tailored. These resonances were found to be related to electric/magnetic dipole (ED/MD) or quadrupole (EQ/MQ) modes for the nanodisks [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Other works regarding Mie resonator design have been reported [2][3][4][5][6], in which the individual modes were distinguished for the resonators and it was shown that these modes can be tuned (shifted, separated, combined or suppressed) by optimizing the nanoparticle shape, diameter and height and the RI of the surrounding medium. It was indicated that the driving mechanism for the in-plane magnetic dipole is due to the coupling of the electric component of the electromagnetic field to displacement loops (vertically oriented inside the (nano)particle). A MD moment, perpendicular to the electric field polarization, is induced by this displacement loop. For this, significant retardation of the driving field is required throughout the particle. The ED resonances require only collective polarization of the inside material of the resonator caused by the incidental light electric field component. Far-field signatures of these resonances can be observed. Scattering cross-section analysis can be used to identify the occurrence/behavior of the individual Mie resonances [3][4][5][6]. In this work, reflectance/transmittance spectra were used where modulation effects of these spectra could be influenced by interference of the Mie resonances with the incident light.
Nanostructuring of Si, including nanodisk-based metasurfaces [8][9][10][11][12][13][14][15][16][17][18][19][24][25][26][27][28], is widely reported in literature due to its attractive features, e.g., its mature fabrication/processing technology, suitable electrical and optical properties, low cost and non-toxicity. While the etching of c-Si nanodisk (array) structures is well-known, transferring the etched nanostructures to other substrate surfaces can still be an issue. In comparison, very few works have addressed the fabrication and optical properties of amorphous silicon (a-Si) nanodisks [18]. Due to the typically large thickness of the (common) c-Si layers, it is unsuitable to create substrate-free structures. For high aspect ratio structures (e.g., nanopillars or nanowires) it is possible to 'break/scrape-off' the structures from the substrate. For the fabrication of substrate-free low aspect ratio Si nanodisks, silicon on insulator (SOI) can be used for etching the patterns and where the insulator (typically SiO 2 ) can be sacrificially etched away.
An alternative way is to deposit a layer of a-Si on a sacrificial layer/substrate surface. The typical RI of a-Si is ~3.6-4.5 in the UV-NIR part of the wavelength spectrum, and has a reported bandgap of ~1.1-1.5 eV. For large scale production, the advantage of a-Si is its low cost and possibility for low temperature layer deposition. Plasma-enhanced chemical vapor deposition (PECVD) of a-Si(:H) is possible at temperatures between 30 and 300 °C, which makes this low temperature processing available for substrate materials like glass, plastics and metals. This paves the way for integration of nanodisk-based metasurfaces in a broader scope of material combinations than has been reported. Furthermore, the choice of a-Si for nanodisk fabrication has advantages compared to using SOI since the a-Si can, in priniciple, be deposited on any type of (sacrificial) layer with better flexibility over the design of the layers.
Dielectric metasurfaces composed of a-Si nanodisk arrays can be used for omnidirectional broadband anti-reflection and optical (filter) applications. In the first case, when they are placed on a high RI substrate (e.g., c-Si), surface reflections can be significantly reduced due to strong forward scattering into the substrate, and thereby increasing the absorption in the substrate (e.g., as in solar cells). On the other hand, when they are placed on/embedded in a low RI (transparent) medium (e.g., SiO 2 or polydimethylsiloxane (PDMS)), coloring in the reflectance mode can be obtained, determined by the geometrical properties of the nanodisks and their array period. Similarly, in transmission mode these a-Si nanodisk metasurfaces have interesting properties for transmission filter applications. Both the reflectance and transmittance peaks of such metasurfaces can be tuned for the (visible-)NIR wavelength region.
In this work, we report the fabrication and optical characterization of a-Si nanodisk (Mie resonator) arrays. Substrate-free a-Si nanodisk arrays were fabricated with a hexagonal array period of ~500 nm, height of 200 nm and diameters varying between ~180-380 nm. The dimension range of the nanodisks used in this work was chosen due to their ability to support multi-modes; this in order to use the relative spectral location of the occurring Mie resonances for transmission (optical) filter applications. In previous works, most of the reported Mie resonator Si structures were fabricated by either electron beam lithography (EBL) or nanoimprint lithography (NIL). Here, we use a simple method to fabricate nano-sized Mie resonator structures by a cheap, flexible and straightforward method based on a combination of colloidal lithography (CL) and inductively coupled plasma reactive-ion etching (ICP-RIE). The obtained nanodisk arrays placed on top of a c-Si substrate and embedded in PDMS are characterized by finite-difference time-domain (FDTD) simulations and spectrally-resolved specular reflectivity and transmission measurements. The main focus of this work is on the transmittance properties of the a-Si nanodisk arrays embedded in PDMS with regard to possible optical filter applications.

Fabrication of a-Si nanodisk-based metasurfaces
The a-Si layers were deposited by PECVD on a c-Si substrate coated with a SiO 2 layer. The substrate-free a-Si nanodisk arrays were fabricated by CL, dry etching and selective wet etching. Figure 1 shows the schematic of the process steps involved in the fabrication of the a-Si nanodisk-based metasurfaces and Fig. 2 presents representative scanning electron microscopy (SEM) images of the fabrication steps.
First a 100 nm sacrificial SiO 2 layer was deposited on a c-Si (100) wafer by PECVD. Next a 200 nm layer of hydrogenated a-Si (a-Si:H; further on specified as a-Si) was deposited by PECVD (SiH 4 flow of 100 sccm, temperature of 250 °C, RF power of 30 W, pressure of 200 mTorr and a planar (calibrated) deposition rate of ~8.3 nm/min). This a-Si layer thickness specifies the height of the nanodisks. Next, an additional ~55 nm SiO 2 cap layer is deposited by PECVD to improve the wettability of the surface and to provide an additional etch mask layer for the a-Si nanodisk etching. CL was performed using the self-assembly of SiO 2 spheres for surface patterning. Substrate pieces of ~2 cm 2 were prepared and oxygen plasma treatment (O 2 flow of 500 sccm, RF power of 1 kW and process time of 10 min) of the surface was done to improve the monolayer coverage of the SiO 2 spheres. A SiO 2 colloidal particle solution (Sigma Aldrich; 500 nm (5 wt%) in H 2 O) was deposited on the surface and a mild spin coating process resulted in the self-assembly of the SiO 2 colloidal particles in a hexagonally close-packed array coverage ( Fig. 2(a)) in several mm 2 -sized patches, where the size of the particles determines the hexagonal array period of the a-Si nanodisk arrays. For obtaining larger (>1 cm 2 ) single monolayer area coverages, optimization of the CL monolayer coverage is required.
To vary the nanodisk diameter, the self-assembled SiO 2 spheres were size reduced ( Fig.  2(b)) by reactive-ion etching (RIE) using a CHF 3 /Ar-based chemistry (CHF 3 /Ar flow of 20/10 sccm, RF power of 200 W and pressure of 40 mTorr). The 'vertical' etch rate of the SiO 2 spheres was approximately ~20 nm/min. An estimate for the resulting diameter, based on the vertical etch rate, is reported in [29]. Simultaneously, the exposed PECVD SiO 2 thin film layer will be etched (etch rate of ~20 nm/min), resulting in a circularly shaped hard mask underneath the SiO 2 colloidal particles. The extra hard mask layer avoids undesired etching at the top part of the nanodisks; caused by the relatively small contact point of the colloidal particle with the underlying surface. In Fig. 5 (Appendix A) schematics and representative SEM images are included, indicating the influence on the etch shape when the additional hard mask layer is absent.  PDMS was taken from the Dow Corning product information and the small (to no) absorption in PDMS was neglected for the wavelength range that was used. The c-Si substrate and the PDMS slab were taken as semi-infinite, where the a-Si nanodisk array on c-Si is in direct contact with the substrate surface and the top surface of the a-Si nanodisks embedded in PDMS are on the same plane as the PDMS surface. Both those geometries mimic the fabricated structures. Using a plane wave source and periodic boundary conditions, the total reflectivity and transmission was determined for the wavelength range of 400-1000 nm. Polarization effects can be neglected for both the measurements and simulations due to the (near) normal incidence angle of the incident light source. Though, it should be noted that polarization effects should be taken into account when using angular incidence angles.
The fabricated substrate-free a-Si nanodisk arrays on c-Si surfaces and those embedded in PDMS were optically characterized by spectrally-resolved reflectivity and transmission measurements. As discussed earlier, the coverage of the a-Si nanodisks on the sample surface resulted in fields of uniform coverage of typically several mm 2 -sized patches due to colloidal lithography influences. Thus, to overcome inconsistencies a home-built small spot setup was used to investigate the (embedded) nanodisk arrays for the wavelength range 400-1000 nm. Due to different experimental configurations, the spot size was ~350 μm 2 for the specular reflectance measurements (microscope built-in lamp, Andor Shamrock spectrophotometer and Andor Newton CCD; NA = 0.13) and ~900 μm 2 for the specular transmittance measurements (supercontinuum source, fiber setup, lens system and fiber-coupled (diameter = 600 μm) AvaSpec spectrometer.
The surface reflectivity was measured and simulated for the a-Si nanodisk arrays on a c-Si surface. The obtained data confirms the broadband anti-reflection application of this type of metasurfaces where average surface reflections as low as ~7.5% were obtained, which are comparable to the results reported in [2]; where additionally the omnidirectional broadband anti-reflection property of this type of structuring was shown. It should be noted that the obtained surface reflection is not as low as values reported for the state-of-the-art antireflection by direct structuring [31]. Though, an additional dielectric layer coating can further reduce the surface reflections. Additionally, the data show a redshift of the reflectivity dips for increasing disk diameters due to the shifting of the Mie resonances to longer wavelengths [2][3][4][5][6]. The measurements show a good agreement with the simulation data obtained for a-Si nanodisk arrays similar to the fabricated structures. The geometries (nanodisk height of 200 nm and nanodisk diameters of 150-400 nm) and spacing (hexagonal array period of 500 nm) used in this work indicate applications for broadband anti-reflection applications for the spectral range of ~550 to >1000 nm, when placed on a c-Si substrate surface. However, a-Si nanodisks absorb in the visible wavelength spectrum and thus it would be more desirable to use transparent anti-reflection metasurface materials (e.g., TiO 2 ). Since the anti-reflection application is not the main focus of this work, the results are implemented in Fig. 6  (Appendix B). Figures 3(a)-3(c) show the simulation results for the transmittance of the a-Si nanodisk arrays (hexagonal array period of 500 nm and height of 200 nm) embedded in PDMS, where the disk diameter is varied between 150 and 400 nm. Figure 3(a) presents a contour plot (increasing diameter with a step size of 5 nm) for the total transmittance in which the relevant transmittance peak and dip shifts are indicated. Figure 3(b) shows the data taken from the contour plot for a nanodisk diameter of 300 nm where the transmittance peaks and dips are labelled accordingly. Several transmittance peaks are observed which are labelled as T1-4, respectively, and transmittance dips as Tdip1(a&b) and Tdip2(a&b). Tdip1 represents an overlap of Tdip1a and Tdip1b. Tdip2 represents an overlap of Tdip2a and Tdip2b. Figure 3(c) shows the simulated transmittance data taken from Fig. 3(a), indicating the shift of the peaks and dips for nanodisk arrays similar to the fabricated structures. A clear transmittance peak (T1) is observed with a peak value of ~60% and shifts from ~675 to ~850 nm as the nanodisk diameter increases from 200 to 350 nm.   isk arrays y. For the ~275-375 without a lear peak 2), with a increases on data is red to the inter-disk on of the er-disk or n [25,32]. the a-Si d) vs total how the determined values for the shifts of the relevant transmission peaks and dips with regard to the diameter variation and occurring wavelength range for the measured and simulated data, respectively. This data shows an agreement between the measured and simulation data for similar structures. Figure 4(a) shows a schematic sketch of the embedded a-Si nanodisk array in PDMS and Fig. 4(b) the simulated reflectivity, transmission and absorption spectra of the structure. The hexagonal array has a period of 500 nm; the nanodisk height and diameter are 200 and 300 nm, respectively. Figure 4(b) indicates that the transmittance dips (Tdip) can be related to the absorption peaks for the nanodisk arrays embedded in PDMS and are thus an indirect indication for the Mie resonances. The relevant absorption peaks are labelled as peak A1-4, along with the relevant reflectance peaks (R1-3) and transmittance peaks (T1-4). It can be observed that Tdip1a is related to peak A4, Tdip1b to peak A3, Tdip2a to peak A2 and Tdip2b to peak A1. Where peaks A1 and A2 are due to ED and MD modes, respectively; A3 and A4 are due to MQ and EQ modes, respectively (see also Fig. 8 (Appendix D)) [2][3][4][5][6]. Tdip2a&b is additionally overlapping with a strong reflectance peak R1, though the location and shift of the small dips alongside peak T3 are still related to the peaks and shifts of A1 and A2.
Peak T1 or T2 (both a peak value of ~60%) is located between a combination of peaks A3&A4 and A1&A2&R1(or R2), where peak R1 (or R2) can be assigned to a strong reflection (back scattering) peak (see Fig. 4(b)). Peak T3 (peak value of ~30%) is located between peaks A1 and A2 and disappears when both peaks spectrally overlap. Peak T4 (peak value of ~12%) is located between peaks A3 and A4 and disappears when both peaks spectrally overlap. Peak T1 (or T2) is interesting for optical (color/NIR) filter applications for nanodisk diameters varying between ~275-375 nm due to the single peak with relatively high transmittance (see Figs. 3(a) and 3(c)). The average peak shift for peak T1 has been determined to be ~1.50 nm/nm diameter increase for disk diameters increasing from 150 to 350 nm. This indicates that the spectral location of this peak can be tuned.
The occurrence of a strong reflection peak (R1) was also mentioned in previous works on Si nanodisk arrays [12][13][14][15][16][17] and can be used for optical (color) filter applications in the reflection mode. Detailed simulation data regarding the a-Si nanodisk diameter influence on the reflectivity data is added in Fig. 9 (Appendix E). For nanodisk diameters ranging from 150 to 400 nm three reflectance peaks can be distinguished: R1, R2 and R3 (see Fig. 4(b)). Peak R1 (peak value of ~75-80%) shifts from ~725 to >1000 nm for nanodisk diameters increasing from 150 to 325 nm with an average shift rate of ~1.52 nm/nm diameter increase. The meas nanodisk arra nanodisks. W interesting op )NIR region, Fig. 4(b)