Printing Beyond sRGB Color Gamut by Mimicking Silicon

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Cite This: Nano Lett. XXXX, XXX, XXX-XXX

Printing Beyond sRGB Color Gamut by Mimicking Silicon Nanostructures in Free-Space Zhaogang Dong,† Jinfa Ho,† Ye Feng Yu,‡ Yuan Hsing Fu,‡ Ramón Paniagua-Dominguez,‡ Sihao Wang,† Arseniy I. Kuznetsov,‡ and Joel K. W. Yang*,§,† †

Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), 2 Fusionopolis Way, #08-03 Innovis, 138634 Singapore ‡ Data Storage Institute, A*STAR (Agency for Science, Technology and Research), 2 Fusionopolis Way, #08-01 Innovis, 138634 Singapore § Singapore University of Technology and Design, 8 Somapah Road, 487372, Singapore S Supporting Information *

ABSTRACT: Localized optical resonances in metallic nanostructures have been increasingly used in color printing, demonstrating unprecedented resolution but limited in color gamut. Here, we introduce a new nanostructure design, which broadens the gamut while retaining print resolution. Instead of metals, silicon nanostructures that exhibit localized magnetic and electric dipole resonances were fabricated on a silicon substrate coated with a Si3N4 index matching layer. Index matching allows a suppression of substrate effects, thus enabling Kerker’s conditions to be met, that is, sharpened transitions in the reflectance spectra leading to saturated colors. This nanostructure design achieves a color gamut superior to sRGB, and is compatible with CMOS processes. The presented design could enable compact high-resolution color displays and filters, and the use of a Si3N4 antireflection coating can be readily extended to designs with nanostructures fabricated using other high-index materials. KEYWORDS: High-resolution color printing, silicon nanostructures, antireflection coating, Mie resonance, highly saturated colors, Kerker’s conditions

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Silicon is a technologically relevant material for nanostructural color printing due to its high refractive index and low relative intrinsic losses compared to metals. Importantly, Si nanostructures support the excitation of both electric and magnetic resonances.13−15 As a result, they have been used for dielectric metasurfaces,16−20 chirality beam splitters,21 antireflection coatings,22 perfect electric and magnetic mirrors,23,24 and optical holograms.25,26 Silicon was previously investigated as structural color elements, for example, as nanowires that exhibit broad Mie resonances when observed in dark-field scattering microscopy,27−32 periodic nanostructures with diffractive effects,33 and thin films.34 These schemes require large lateral dimensions and/or periodicity and result in reduced print resolutions compared to plasmonic nanostructures. However, the high refractive index of Si, n ∼ 4 in the visible range, enables tightly confined optical modes within the nanostructure, suggesting its untapped potential as multicolor pixels that can be closely packed, nondiffractive, and inherently high resolution.

lasmonic resonances of metallic nanostructures have enabled high-resolution color printing beyond the optical diffraction limit with a resolution of ∼100,000 dots per inch (dpi).1−9 However, as highlighted by a recent review on this technology,8 plasmonic colors suffer from poor color saturation with a gamut that occupies only a small subset of perceivable colors on the International Commission on Illumination (CIE) 1931 chromaticity diagram. As sRGB is the standard color space for computer systems and the Internet,10 wide acceptance of new color technologies would require meeting or surpassing the gamut of sRGB. Though highly saturated colors with plasmonic structures are achievable through diffractive effects,11,12 attempts to preserve resolution and viewing-angle independence have resulted in poor color saturation. Moreover, the use of precious noble metals, such as Au and Ag, may result in increased cost, limiting its potential applications, and is not compatible with complementary metal-oxide semiconductor (CMOS) nanofabrication technology. Despite its CMOS compatibility, reported gamut from Al is generally less saturated than that of Ag, as it supports spectrally broader resonances.2 Hence, extending the range of materials beyond metals could enable new nanostructure designs that retain the high resolution of plasmonic colors while enhancing color saturation. © XXXX American Chemical Society

Received: August 22, 2017 Revised: October 12, 2017

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DOI: 10.1021/acs.nanolett.7b03613 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 1. Nanostructure design and experimental realization of additive colors using Si nanodisks exceeding gamut of sRGB. (a) Schematic of the color pixel design consisting of silicon nanodisks/70 nm thick Si3N4/silicon substrate. The diameter, gap size, and height of the nanodisks are denoted as D, g, and h, respectively. (b,c) Calculated silicon color palette and corresponding International Commission on Illumination (CIE) 1931 chromaticity diagram based on finite-difference time-domain (FDTD) simulations. D varies from 40 to 270 nm, g varies from 10 to 120 nm, h = 130 nm. Calculated colors predict larger color gamut than sRGB triangle. (d,e) SEM image of silicon nanodisks for basic and mixed color palettes, respectively. (f) Bright-field optical micrographs of the basic silicon color palette after thermal annealing at 800 °C for 5 min in nitrogen environment. (g) CIE xy chromaticity coordinates of measured reflectance spectra of color palette occupying ∼120% of the sRGB gamut (see Figure S7 for details).

Kerker’s conditions to saturated color generation is here needed to realize the full potential of Si colors. Here, we introduce a design of silicon nanostructures that achieves highly saturated, viewing-angle independent (up to ±20°), and high-resolution color prints. Silicon nanostructures were fabricated onto a silicon substrate with an index-matched 70 nm thick Si3N4 layer. This antireflective (AR) coated substrate creates a local environment that effectively suspends the Si nanostructures in free-space, establishing a direct correlation between the observed reflectivity and the particles’ backscattering, with its distinctive sharper optical resonances associated with the realization of Kerker’s conditions. To the best of our knowledge, this nanostructure design is unique and distinct in its ability to simultaneously achieve the largest color gamut to date occupying an area larger than the sRGB triangle in the CIE chromaticity diagram, viewing-angle independence, and high-resolution. The straightforward implementation using established CMOS processes could spur the use of resonant nanostructures in compact high-resolution color display and imaging applications. Figure 1 presents the design, simulation, and experimental results of high-resolution and high-saturation color printing.

Despite recent progress in color prints using Si nanostructures,35−39 the resultant colors are invariably limited in saturation and gamut, due to substrate effects. Namely, the Q-factor of the resonances observed in reflection drops significantly in the presence of a substrate, such as quartz, and worsens as the refractive index of the substrate increases. In stark contrast, single particles in free-space supporting magnetic and electric dipole resonances can exhibit narrow spectral transitions from zero backward to suppressed forward scattering, that is, satisfying Kerker’s first and second conditions.40 This effect could produce transitions in the reflectance spectra that are far narrower than the electric and magnetic dipole resonances themselves, which is desirable based on Schrodinger’s color theory.41 The unrealistic condition of particles in free-space have been approximated in the visible spectrum with nanostructures weakly attached to a substrate,42 or embedded in homogeneous media,43,44 and in the microwave regime with centimeter-scale objects held by microwave-transparent polystyrene45 demonstrating Kerker’s directional scattering. Hence, a practicable system that closely mimics nanostructures in free-space and gainfully applies B

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Figure 2. Optical characteristics of silicon nanostructures placed onto an AR-coated substrate mimicking the illumination conditions of particles in free-space. (a) Schematic illustration the nanostructure/substrate design and its optical equivalence to nanostructures suspended in free space. (b,c) Simulated reflectance spectra of silicon nanodisks (D = 130 nm and g = 70 nm) as placed onto an AR-coated substrate and free-space, respectively. (d,e) Multipolar decomposition calculations of the scattering cross sections, σscattering, for the md, ed, mq, and eq modes. (f,g) Individual phases of the excited md and ed, as retrieved from the multipolar decomposition. The first Kerker’s condition is exactly satisfied at the reflectance dip wavelength. The reflection peak appears close to where the seconds Kerker condition is approximately fulfilled. (h,i) Spatial distributions of the simulated electrical field magnitude (|E|) and magnetic field magnitude (|H|), for silicon nanostructures placed onto an AR coated silicon substrate and in freespace. Scale bars correspond to 50 nm.

od.17 A layer of 30 nm thick hydrogen silsesquioxane (HSQ) resist (Dow Corning, XR-1541-002, 2% dissolved in methyl isobutyl ketone) was spin coated onto the sample surface at 5k rpm, followed by electron beam lithography and dry etching processes.46 The detailed fabrication process is shown in Figure S2 and the resultant color palette is shown in Figure S3. Figure 1d,e presents the scanning electron micrograph (SEM) images of the fabricated silicon color pixels made of nanodisks for both the basic and mixed color palettes, respectively. Finally, the sample was annealed in a rapid thermal processing (RTP) system at 800 °C for 5 min in a nitrogen environment. The optical micrograph of the final sample is shown in Figure 1f (see details in Characterizations). It can be seen that color pixels with a range of highly saturated colors on a dark background were achieved with a close agreement with the calculated colors. To demonstrate viewing-angle independence, the color palette was imaged through objective lenses of different

Specifically, Figure 1a shows the detailed schematic of the “color pixels” made of silicon nanostructures, that is, nanodisks. In addition, Figure 1b presents the simulated silicon color palette of silicon nanodisks using finite-difference time-domain (FDTD) method at normal incidence, where the gap size g is varied from 10 to 120 nm and the disk diameter D is varied from 40 to 270 nm. The height of the nanodisks h is 130 nm. On the basis of the simulated reflectance spectra of silicon nanostructures, the corresponding CIE chromaticity diagram is shown in Figure 1c, where the colors of the designed silicon pixels are predicted to occupy 120% of the “sRGB” triangle in the CIE chromaticity diagram (see Figure S1 for details). To realize this design, we fabricated silicon nanostructures using high-resolution electron-beam lithography and reactiveion etching. Briefly, a 130 nm-thick amorphous silicon layer was grown onto a silicon substrate with a 70 nm thick Si3N4 layer (⟨100⟩ orientation, from MOS Group Pte. Ltd.), using the plasma-enhanced chemical vapor deposition (PECVD) methC

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Figure 3. Resonant modes of the best “red”, “green” and “blue” color pixels. (a−c) Reflectance spectra for the best red (D = 170 nm and g = 90 nm), green (D = 130 nm and g = 70 nm) and blue (D = 40 nm and g = 50 nm) pixels, respectively, with corresponding SEM images of the silicon nanodisks shown in the insets. (d−f) Simulated optical reflection spectra for the silicon nanodisks corresponding to cases (a−c), respectively. Insets are the experimentally obtained optical images corresponding best red, green, and blue color pixels, extracted from Figure 1f. (g−i) Simulated spatial distribution for both the electrical field magnitude (|E|) and magnetic field magnitude (|H|). The scale bars denote 50 nm.

Numerical Simulations and Figure S7). Improvements of color vibrancy were observed after the annealing process (see Figures S3 and S7) plausibly due to the crystallization of Si and a reduction in optical losses.47 Slight discrepancies exist between the simulated and experimental color palettes in the cases of closely spaced large disks (large D, small g) and sparsely spaced small disks (small D, large g). These discrepancies originate from the proximity effects of the electron beam lithography. For closely spaced large disks, the structures tend to be overexposed to the electron-beam, because of the dense neighboring large disks. In contrast, sparsely spaced small disks tend to be underexposed. In the actual experiments, we used a single exposure dose that is optimal for the majority of the silicon nanodisks. Proximity effect correction techniques can be applied (despite increased complexity/exposure time) to circumvent this problem.48 The schematic in Figure 2a illustrates the role of the 70 nm Si3N4 antireflection layer for the silicon color pixel. The introduction of an antireflective layer effectively creates a

numerical apertures, hence varying the angle of the collection cone (see details in Figure S4), and varying tilt angles (see details in Figure S5). The results show that when the collection angle was varied from 8.6° (i.e., NA = 0.15) to 26.7° (i.e., NA = 0.45), the colors were not affected and were independent of the viewing-angle. It is seen that the colors strongly depend instead on the disk diameter D (and not on the spacing) of the silicon nanostructure (see detailed reflectance spectra in Figure S6). In addition, Figure S6d,f presents the characterization results of silicon nanodisks with a fixed diameter of 130 nm but patterned with a position jitter, where the gap size g was randomly varied from 30 to 110 nm, to further confirm this observation. The color gamut of the fabricated palette was obtained by measuring the absolute optical reflectance spectra of each color swatch using a microspectrophotometer (CRAIC UV−vis-NIR QDI 2010, 36× objective lens, NA = 0.50) and mapping the corresponding coordinates onto the CIE plot. Figure 1g shows that the experimentally generated colors occupy ∼121% of the sRGB triangle in the CIE chromaticity diagram (see details in D

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Figure 4. Nondiffractive colors from small groups of nanostructures. (a,b) Optical and scanning electron micrographs of checkerboard patterns consisting of 2 × 2 nanodisks with diameters of 180 and 80 nm and with center-to-center distance of 250 nm. (c,d) Optical micrograph and SEM for checkerboard with 5 × 5 nanodisks. Under identical illumination conditions, both 2 × 2 and 5 × 5 groups of nanostructures exhibit similar color schemes, linked only to dimensions of individual nanostructures and not to array size.

(eq) modes are excited in the silicon nanostructures, as shown in Figure 2d,e with the corresponding phases of md and ed shown in Figure 2f,g. These simulations show that the first Kerker’s condition is fully met (with md and ed having equal amplitude and phase) resulting in a total suppression of backscattering at the observed reflectance dip. In addition, the observed reflection peak appears close to the point where md and ed have equal amplitude but are out of phase. At this point, the second Kerker condition is approximately fulfilled, as the phase difference is not exactly π. While this peak in the backscattering does not follow directly from the realization of Kerker’s second condition, for silicon particles these two situations are typically spectrally close, as has been shown theoretically for silicon nanospheres in free-space.50 Striking similarities are seen in the electric and magnetic field distributions for nanostructures on AR coated substrates (Figure 2h) and in free-space (Figure 2i). Substrate effects are investigated with structures on Si and quartz. Figure S9 presents the chromaticity diagram of a reference structure without the Si3N4 layer, that is, silicon nanodisks etched directly into a silicon substrate. The dramatic difference in the CIE plots of Figure S9c and Figure 1f highlights the important role of this dielectric layer in achieving highly saturated colors. The results are not improved even with nanostructures fabricated on transparent substrates such as quartz (see Figure S10 for details). Substrate effects are thus a hindrance to achieving a wide color gamut. Interestingly, the substrate effect can also be brought back in our system by

substrateless environment for the particles, thus circumventing the issue of Q-factor reduction due to mode leakage into the substrate. As a result, the Si nanostructures behave as if they were suspended in free space. This effect restores the direct correlation between the backscattering spectra from the particles with its narrow features. The designed Si3N4 layer provides a simple index matching coating based on the following calculations: A single-layer antireflection coating requires an index that is the geometric mean of silicon and air (i.e., nsinair ) with a quarter-wave thickness. As the refractive index of silicon is ∼4 in the visible spectral region, the refractive index n of the spacer layer should be ∼2, close to that of Si3N4. Taking a central wavelength λ0 of ∼560 nm in the visible range, the thickness of the Si3N4 layer should be ∼70 nm, that is, λo 4n

(see details in Figure S8). Further improvements to this simple index-matching layer could be achieved with a multilayer design49 to enable perfect matching across the visible spectrum. To illustrate the importance of this antireflection (AR) coating, we analyzed the detailed optical characteristics of a representative color pixel with diameter D = 130 nm and gap size g = 70 nm. Figure 2b,c presents the simulated optical reflectance spectra for silicon nanostructures placed onto the AR-coated substrate and in free-space, respectively, using the finite element method (FEM) implemented in COMSOL (details in Numerical Simulations). Multipolar decomposition was performed, showing that the magnetic dipole (md), electric dipole (ed), magnetic quadruple (mq), and electric quadruple E

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Figure 5. High-resolution color printing of art pieces using silicon nanodisks. (a) Original image of “Murnau Street with Women” by Vasily Kandinsky. (Reprinted with permission Copyright 2017 Artists Rights Society (ARS), New York.) (b,c) Optical microscope image of the fabricated picture using silicon nanodisks before and after annealing process in a nitrogen environment. The scale bar in the optical microscope images is 20 μm. (d) SEM image of the selected region highlighted by the white dot rectangle in (c). The scale bar in the SEM image is 1 μm.

affecting the index-matching condition. By coating the structures with a layer of immersion oil with a refractive index of 1.51, the saturated colors are suppressed and the gamut decreases, as shown in Figure S11. Figure 3 presents the experimental and theoretical investigations on the best red, green, and blue pixels obtained with the proposed system. Figure 3a presents the measured reflectance spectrum of the best red pixel (D = 170 nm and g = 90 nm) with the corresponding SEM of the silicon nanodisks shown inset. The corresponding simulated reflectance spectrum is shown in Figure 3d with the optical micrograph of the red pixel array shown inset. The simulated field distributions for the ed and md modes at the spectral peaks are shown in Figure 3g,h. Kerker’s conditions are also satisfied at the dip and peak of the spectrum for the red pixel, as shown in Figure S12. Unlike green and red, the narrow structures that generate blue predominantly support ed resonances, as evident in the lack of the md mode in the field distributions shown in Figure 3i. Pixels approximating “white” and “black”, and further broadening of the gamut can be achieved by geometric control. As the nanodisk diameter is increased beyond 170 nm, the red color quality gives way to a neutral tone, as colors drift toward the central region of the CIE plot (see Figure S13, for nanodisks with D = 270 nm and g = 30 nm). Conversely, “black” pixels are achieved using nanodisks with D = 80 nm and g = 100 nm (see Figure S14). Lastly, we also investigated the color palette obtained from silicon nanorings and silicon nanodisks with color mixing (see Figure S15), where more colors in the CIE plot could be obtained. To investigate if colors arise from local resonances in subwavelength groups of structures without requiring multiple repetitions of the unit-cells or any diffractive effects, we

fabricated two different diameters of Si nanodisks in a checkerboard pattern. The subdiffraction characteristics of the designed silicon color palette is demonstrated in Figure 4a, showing an optical microscope image of the checkerboard test pattern captured by a 150× objective lens (NA = 0.90). This pattern is printed with a resolution of 101,600 disks per inch (∼100,000 dpi), that is, one silicon disk every 250 nm. Figure 4b shows the corresponding SEM image of the basic checkerboard pattern, which consists of nanodisks with diameters of 180 and 80 nm, respectively. It shows that the individual silicon nanodisks are able to exhibit their respective colors. Increasing the number of disks per square to 5 × 5 nanodisks did not change the color scheme of the checkerboard, but merely reduced the mixing of the colors, as shown in Figure 4c,d. Finally, we use the silicon nanodisks to achieve a highresolution print of an art piece with highly saturated colors. Figure 5a presents the original image of the art piece “Murnau Street with Women” by Vasily Kandinsky. (Reprinted with permission. Copyright 2017 Artists Rights Society (ARS), New York). We first color matched this image pixel-by-pixel to the experimentally realized color palette in Figure 1f. Colors were fitted based on the least mean square error in the “R-G-B” values. When creating the exposure file for electron beam lithography, we used an average pixel size of 650 nm (∼40,000 dpi) containing multiple nanodisks (details in EBL Layout Creation). A universal pixel size would have created gaps between pixels as there will be regions where the pixel size is not an integer multiple of the desired pitch size. For example, the chosen pixel size of 650 nm is not a multiple of the pitch Λ for the best green color pixel (D = 130 nm and g = 70 nm), which has a pitch Λ of 200 nm. To resolve this problem, we F

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Nano Letters implemented a new “adaptive” pixel method, where the local pixel is resized based on the pitch of the fitted color pixel. Figure 5b,c presents the optical microscope image of the nanoprinted art piece based on silicon nanodisks before and after the annealing process, where the image demonstrates the color saturation of our nanostructure design. By comparing Figure 5a−c, it can be observed that the achieved colors in the fabricated image are close to the original image, further demonstrating that individual color pixels that compose the image accurately match the colors picked from the large arrays in the palette. Note that the blue colors on the distant house wall as highlighted by the white dot rectangle, which was missing in the preannealed structures, were reinstated after the annealing process. The remaining color mismatch is attributed to the electron-beam proximity effects during the exposure, resulting in size discrepancies between the designed and patterned nanodisks. We introduce a new metric, that is, area coverage of the CIE chromaticity diagram, to quantify the color gamut. We applied this metric to compare the color gamut in this manuscript, with an area ratio of 121% with respect to sRGB, and the Al color palettes from a previous work,2 with an area ratio of 17% with respect to the sRGB area. In addition, a more complete quantification in color saturation should also consider the overlap between the achieved color gamut and sRGB. In this manuscript, the achieved color gamut has a 78% overlap with sRGB, as the generated colors do not cover points close to the red−blue side of the sRGB triangle. The current limitation in our design is the significant reflection from the substrate particularly in the blue region, thus affecting the red and green colors. We suspect that the fundamental limit in color saturation might lie in sharpness of the transition from forward to backward scattering with the utilization of Kerker’s generalized conditions. While there have also been reports of vibrant color palettes based on TiO 2 metasurfaces, 51 the supported optical resonances of TiO2 nanostructures are not well confined and are spectrally close to the first diffraction order due to the comparatively low refractive index of TiO2. Diffractive effects contribute to the color vibrancy in these structures, resulting in a compromise of the viewing angle. In contrast, Si has larger refractive index than TiO2, pushing the supported optical resonances far from the first diffractive order spectrally. The colors from the Si nanostructures are also diffraction independent, and these contribute to the expanded viewing angle of our system. In conclusion, the combination of low intrinsic loss of Si and the design of Si nanostructures on an AR-coated substrate has produced “additive” colors that are highly saturated with a gamut covering ∼121% of the sRGB triangle in the CIE plot. To the best of our knowledge, the results represent the highest color quality achieved by nanostructures that support print resolutions of ∼100,000 dpi and encompass all technologyperformance indicator parameters for color printing.8 The presented concepts will potentially enable highly saturated and high-resolution color integration in digital imaging with full CMOS compatibility with larger gamuts made possible using engineering of antenna modes, better antireflection layers, and other high-index materials. CVD Growth of Silicon, HSQ Mask Fabrication, Silicon Etching, and Silicon Annealing. Amorphous silicon with a thickness of 130 nm was grown on a silicon substrate with a 70 nm thick Si3N4 layer, by using plasma-enhanced chemical vapor

deposition (PECVD) method.17 Real and imaginary parts of refractive index for the grown silicon films have been measured by using ellipsometry across the whole visible spectrum.17 A hydrogen silsesquioxane (HSQ) mask was fabricated on top of the silicon substrate using electron beam lithography (EBL, Elionix ELS-7000).46 Before the electron beam exposure, HSQ resist with a concentration of 2% wt, diluted in methyl isobutyl ketone (MIBK, Dow Corning XR-1541 E-beam resist), was spin coated onto the cleaned silicon substrate at 5 krpm giving the resist thickness of ∼30 nm. The electron beam exposure was carried out with the following conditions: electron acceleration voltage of 100 keV, beam current of 200 pA, and the exposure dose of ∼12 mC/cm2. The sample was then developed in a NaOH/NaCl salty solution (1% wt/4% wt in deionized water) for 60 s and immersed in deionized water for 60 s to stop the development.52 Next, the sample was immediately rinsed in acetone followed by isopropanol alcohol (IPA) and dried by a continuous flow of nitrogen air gun for 1 min. With the HSQ protection mask, silicon etching was done using inductively coupled-plasma (ICP, Unaxis shuttle lock system SLR-7701-BR).46 During the ICP etching process, the experimental conditions were a direct current power of 150 W, a coil power of 300 W, Cl2/HBr with flow rates of 18 and 22 standard cubic centimeters per minute (sccm), process pressure of 10 mTorr, temperature of 6 °C, and an etching time of 34 s. After the silicon etching process, the HSQ resist was removed using hydrofluoric (HF) acid. EBL Layout Creation. The color image of the painting in bmp format was first loaded into MATLAB with the “R”, “G” and “B” matrices. Then, the color at each pixel of the image was fitted based on the least mean square error with respect to the basic silicon color palette shown in Figure 1f; at the same time, the information on the silicon nanodisks, that is, diameters and gap sizes, was recorded during the fitting process. Next, we converted the recorded silicon nanodisk information into the layout of silicon nanostructures with the chosen 650 nm pixel size. During the implementation process, a problem may arise, namely, that the chosen pixel size may not be a multiple of the pitch size of the designed color pixel. To solve this problem, we have introduced a new “adaptive” meshing method, where the local mesh size adapts based on the respective pitch size of the chosen color pixel. Characterizations. The optical reflectance spectrum of the fabricated silicon nanostructures was measured using a CRAIC UV−vis-NIR microspectrophotometer QDI 2010 (36× objective lens with a numerical aperture of 0.5) with the polarized broadband light source. The absolute reflectance spectra were obtained because we calibrated our reflectance measurements with respect to a certified standard calibration sample from CRAIC Technologies (http://www.microspectra.com/). Moreover, for the image acquisition of the color palette Figure 1f and Figure 5b,c, a white color balancing was first carried out on a 300 nm thick aluminum film as evaporated onto silicon substrate by using e-beam evaporation (Denton evaporator, 5 × 10−7 Torr, evaporation rate of 0.5 Å/s).53 Next, the optical microscope images in Figure 1f and Figure 5b,c were taken using an Olympus microscope (MX61) with a software of “analySIS”, a 10× objective lens (MPlanFL N, NA = 0.3), a camera (Olympus SC30) with an integration time of 12 ms, and broadband halogen light source (U LH100 3, 100 W) with a linear polarizer (U-AN360−3). The scanning electron microscope (SEM) images were taken with an electron acceleration voltage of 10 keV. G

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Nano Letters Numerical Simulations. Finite-difference time-domain (FDTD) simulations were carried out using a commercial software (Lumerical FDTD Solutions). Periodic boundary conditions were used and the incident optical field is linearly polarized along x-direction with a normal incidence condition. A nonuniform meshing technique was applied with a minimum mesh size down to 0.5 nm. The dielectric function of crystalline silicon was taken from the handbook by Palik.54 In addition, the International Commission on Illumination (CIE) 1931 chromaticity diagram is calculated based on the color matching functions (see details in Figure S16). The area of the silicon color pixels spanning over the CIE chromaticity diagram was calculated through fitting of a smooth free shape in Origin software. For the color palette in Figure 1b, first, FDTD method was applied to simulate the optical reflectance spectra from the silicon nanodisks with the respective diameters and gap sizes. Next, the simulated reflectance spectra for each color pixel is then converted to XYZ coordinate in the CIE 1931 plot (see details in Figure S16). After that, the colors were then plotted out by using Mathematica’s XYZColour function, as shown in Figure 1b. Moreover, in order to identify the modes being excited within the silicon nanostructures, we have applied a multipolar decomposition of the polarization currents as excited within the structures, which are directly related to the internal optical fields. This approach takes into account all interparticle interactions, as well as the presence of the substrate. To perform the multipolar decomposition, FEMbased simulations were done using COMSOL. We simulated a single unit-cell with periodic boundary conditions. An injection port was used to excite the system with a normally incident plane wave and the reflection and transmission coefficient were calculated using additional ports (one for each diffraction mode supported by the system). The obtained results agree well with those obtained by FDTD. The resulting fields excited in the particle were then used to perform the multipolar decomposition.55,56 A Cartesian basis was used in this decomposition with the center coinciding with the center of mass of the particles. The set of electric multipoles was corrected by taking into account of the radiation interference with the family of toroidal moments and mean-square radii distributions. The phases shown in Figure 2 correspond to the individual phases of the only nonzero components of the corrected electric and magnetic dipoles, directed along the incident electric and magnetic fields, respectively. The detailed explicit expressions could be found in the Supporting Information Section 17.

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silicon color palette with an immersion oil, multimode decomposition simulations, silicon nanodisks for approximating white color pixel, silicon nanodisks for black pixel, color palettes by silicon nanorings and silicon nanodisk mixing, color matching functions, and multipolar decomposition technique (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: +65 64994767). ORCID

Zhaogang Dong: 0000-0002-0929-7723 Arseniy I. Kuznetsov: 0000-0002-7622-8939 Joel K. W. Yang: 0000-0003-3301-1040 Author Contributions

Z.D., A.I.K., and J.K.W.Y. conceived the concept. Z.D. and J.K.W.Y. designed the experiments, fabricated and characterized the samples, and wrote the manuscript. J.F.H. performed the finite-difference time-domain simulations and the calculation of the CIE color coordinate. Y.F.Y. performed the growth of the silicon films by using CVD method. Y.H.F. initiated the concept of using silicon nanorings for color pixels. R.P.-D. performed the COMSOL simulations, the multipolar decomposition analysis and provided theoretical support. S.W. did the initial FDTD simulations. All authors analyzed the data, read, and corrected the manuscript before the submission. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to acknowledge the funding support from Agency for Science, Technology, and Research (A*STAR) SERC Pharos project (Grant 1527300025). In addition, Z.D. and J.K.W.Y. also acknowledge the funding support from A*STAR Young Investigatorship (Grant 0926030138), SERC (Grant 092154099), National Research Foundation Grant Nos. NRF-CRP001-021, NRF-CRP 8-2011-07, and A*STAR-JCO under Project Number 1437C00135. Furthermore, Z.D. also would like to thank J. Deng, E. X. Tang, and V. S. F. Lim from the Institute of Materials Research and Engineering, A*STAR, for technical assistance.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b03613. Area fitting of the simulated silicon colors in the CIE chromaticity diagram, fabrication process, silicon color palette after the dry etching process, influence of numerical aperture on the silicon color palette, influence of the tilt angle on the silicon color palette, influence of the silicon nanodisk diameter and gap sizes, area fitting of silicon color palette after annealing in the CIE chromaticity diagram, flat silicon substrate with 70 nm thick Si3N4 layer, silicon nanodisks on silicon substrate without 70 nm thick Si3N4 layer, chromaticity diagram as generated by silicon nanodisks on quartz substrate, H

DOI: 10.1021/acs.nanolett.7b03613 Nano Lett. XXXX, XXX, XXX−XXX

Letter

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DOI: 10.1021/acs.nanolett.7b03613 Nano Lett. XXXX, XXX, XXX−XXX