Supporting Information for: Printing Beyond srgb Color Gamut by Mimicking Silicon Nanostructures in Free-Space Zhaogang Dong 1, Jinfa Ho 1, Ye Feng Yu 2, Yuan Hsing Fu 2, Ramón Paniagua-Dominguez 2, Sihao Wang 1, Arseniy I. Kuznetsov 2, and Joel K. W. Yang 3,1, * 1 Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), 2 Fusionopolis Way, #08-03 Innovis, 138634 Singapore 2 Data Storage Institute, A*STAR (Agency for Science, Technology and Research), 2 Fusionopolis Way, #08-01 Innovis, 138634 Singapore 3 Singapore University of Technology and Design, 8 Somapah Road, 487372, Singapore *Correspondence and requests for materials should be addressed to J. K. W. Y. (email: joel_yang@sutd.edu.sg; telephone: +65 64994767). S1
S1. Area fitting of the simulated silicon colors in the CIE chromaticity diagram. Figure S1. Area fitting of the simulated silicon colors in the CIE chromaticity diagram. The area of the srgb in the CIE plot is calculated to be 0.11205. The area of the simulated color palette is 0.13451, which is 120% of the srgb areal coverage. S2
S2. Fabrication process of silicon nanodisks on silicon substrate with a 70-nm-thick Si 3 N 4 layer for high-resolution color printing beyond the diffraction limit. Figure S2. Fabrication process of silicon nanostructures for vibrant high-resolution color printing. (a) Hydrogen silsesquioxane (HSQ) resist spin coated onto the silicon substrate with a 70-nm-thick Si 3 N 4 and 130-nm-thick silicon layers. (b) E-beam exposure to fabricate the HSQ resist mask. (c) Inductively-coupled plasma (ICP) for silicon etching with Cl 2 /HBr gases. (d) HSQ resist removal by hydrofluoric (HF) acid (5%) for 30 seconds. S3
S3. Silicon color palette after the dry etching process. Figure S3. Silicon color palette after the dry etching process (before annealing). (a) Optical microscope image of the basic silicon color palette after the dry etching process (before annealing). (b) CIE plot of the silicon colors as obtained experimentally, in comparison with the simulated silicon colors and srgb triangle. The area of the srgb triangle in the CIE plot is calculated to be 0.11205. The area of the simulated color palette is 0.13451, which covers an area 20% larger than that covered by the srgb triangle. In addition, the area for the experimental silicon color palette (without annealing) is 0.12347, which is 110% of the srgb areal coverage. (c) Measured reflectance spectrum of the silicon color pixels with diameter of 130 nm and gap size of 60 nm, as highlighted by the white dotted square in Fig. S3a. S4
S4. Influence of numerical aperture on the silicon color palette. Figure S4. Optical image of silicon color palette as captured by objective lenses with different numerical apertures (NAs). (a)-(c) Optical microscope image of the silicon color palette after annealing as captured by using objective lenses with NA of 0.15, 0.30 and 0.45, respectively. It shows that the numerical aperture of objective lens has little influence on the colors of the silicon color palette. Thus, optical diffraction effects are not involved in the generation of colors. During the capturing process of these optical images, the integration time of the charge-coupled device (CCD) camera is kept to be the same at 12 msec. S5
S5. Influence of the tilt angle on the silicon color palette. Figure S5. Influence of the tilt angle on the silicon color palette (after annealing process). (a)-(b) Optical microscope image of the silicon color palette as captured by a 20 objective lens with a tilt angle of 0 degree and 20 degrees, respectively. In b, due to the tilt angle, some pixels were slightly defocused. S6
S6. Influence of the silicon nanodisk diameter and gap size on the optical resonances. Figure S6. Influence of the gap size between silicon nanostructures on the corresponding optical resonances. (a) Optical microscope image of the silicon color palette. (b)-(c) Measured and simulated reflectance spectra of the silicon nanodisks with diameters of 130 nm and a varying S7
gap sizes from 10 nm to 120 nm. It shows that the structural color is mainly dependent on the silicon nanodisk diameter, although the gap size between silicon nanodisks will slightly affect the optical coupling between neighboring units. (d)-(e) SEM image and optical reflectance spectra of silicon nanodisks with a diameter D of 130 nm and position jitter, such that the interparticle gaps g are randomly distributed from 30 nm to 110 nm. The inset figure in Fig. S6e shows the corresponding bright-field optical microscope image of the color pixel. This fabricated nanostructure strengthens the claim that the silicon color pixel as demonstrated in the manuscript originated from single nanostructures in isolation. S8
S7. Area fitting of silicon color palette after annealing in the CIE chromaticity diagram. Figure S7. Area fitting of silicon color palette after annealing in the CIE chromaticity diagram. The area of the srgb area in the CIE plot is calculated to be 0.11205. The area of the simulated color palette is 0.13451, which is 120% of the srgb areal coverage. In addition, the area for the experimental silicon color palette is 0.13535, which is ~121% of the srgb areal coverage. S9
S8. Flat silicon substrate with 70-nm-thick Si 3 N 4 layer. Figure S8. Flat silicon substrate with 70-nm-thick Si 3 N 4 layer. (a) Schematic of the flat silicon substrate with 70-nm-thick Si 3 N 4 layer. (b) Experimentally measured reflectance spectra of the flat silicon substrate with 70-nm-thick Si 3 N 4 layer. The dip wavelength is around 560 nm. (c) Simulated optical intensity distribution using finite-difference time-domain (FDTD) method to show the intensity distribution at the dip wavelength 550 nm. It shows that there is no reflection back to air region, since there are no interference fringes in the air region. S10
S9. Silicon nanodisks on silicon substrate without 70-nm-thick Si 3 N 4 layer. Figure S9. Silicon nanodisks on silicon substrate without 70-nm-thick Si 3 N 4 layer. (a) Schematic illustration of silicon nanodisks on silicon substrate with the labeled geometrical parameters, diameter D, height h, and gap size g. (b) Optical microscope image of the silicon nanodisks on silicon substrate. The height h was 130 nm. The nanodisk diameter D was varied from 40 nm to 150 nm, and the gap size g was varied from 10 nm to 120 nm. (c) CIE plot of the corresponding colors based on the measured reflectance spectra. It shows that the colors are very close to the central white region in the CIE plot. S11
S10. Chromaticity diagram as generated by silicon nanodisks on quartz substrate. Figure S10. Chromaticity diagram generated by silicon nanodisks on quartz substrate after annealing. (a) Schematic illustration of silicon nanodisks on quartz substrate with the labeled geometrical parameters, diameter D, height h, and gap size g. (b) Optical microscope image of the silicon nanodisks on quartz substrate. The height h was 130 nm. The nanodisk diameter D was varied from 40 nm to 150 nm, and the gap size g was varied from 10 nm to 120 nm. (c) CIE plot of the corresponding colors based on the measured reflectance spectra. It shows that the generated colors in this case are worse than the proposed design based on silicon nanostructures on top of silicon substrate with a 70-nm-thick Si 3 N 4 layer, as shown in Fig. 1f. S12
S11. Silicon color palette with an immersion oil with a refractive index of 1.5146. Figure S11. Silicon color palette coated with an immersion oil with a refractive index of 1.5146. (a) Optical microscope image of the silicon color palette covered with immersion oil taken with x10 objective lens (NA=0.30). (b) CIE plot of the corresponding silicon colors. (c) Measured optical reflectance spectra of the color pixel with a diameter of 130 nm and gap size of 60 nm. S13
S12. Multimode decomposition simulation for the best red, green and blue color pixels. Figure S12. Simulated reflectance spectra for best red, green and blue color pixels by using COMSOL and multipole decomposition method. Dimensions of these color pixels are shown in Fig. 3. (a)-(c) Simulated optical reflectance spectra by using COMSOL method for the best red, green and blue color pixels. (d)-(f) Multimode decomposition method to reveal the scattering cross-section of the respective optical modes (i.e. magnetic dipole, electrical S14
dipole, magnetic quadrupole, electrical quadrupole) being excited on the respective silicon nanostructures. (g)-(i) Multipolar decomposition method to reveal the optical phase of the magnetic dipole and electrical dipole, respectively. It shows that 1 st Kerker s condition has been satisfied for the red and green color pixels at the dip wavelength. The observed reflection peak appears near to the wavelength of satisfying 2 nd Kerker s condition approximately, which has been theoretically investigated for silicon nanoparticle in free-space. 1 S15
S13. Silicon nanodisks for approximating white color pixel. Figure S13. Silicon nanodisks (D=270 nm and g=30 nm) for approximating the white color pixel. This color pixel is closest to the central white region in the CIE diagram. (a) Optical reflectance spectra of the pixels with the inset optical microscope image. (b) Scanning electron microscope (SEM) image of the silicon nanodisks. (c) Spatial distribution of electrical field magnitude E and magnetic field magnitude H, by using finite-difference time-domain (FDTD) method. The scale bar denotes 50 nm. S16
S14. Silicon nanodisks for black pixel. Figure S14. Silicon nanodisks (D=80 nm and g=100 nm) for black color pixels. (a) Optical reflectance spectra of the black pixels with the inset optical microscope image. (b) Scanning electron microscope (SEM) image of the silicon nanodisks. (c) Spatial distribution of electric field magnitude E and magnetic field magnitude H at the respective wavelengths, by using finite-difference time-domain (FDTD) method. The scale bar denotes 50 nm. The intensity distributions show that the optical energy are absorbed by the silicon nanodisks, at red, green and blue wavelengths. S17
S15. Color palette by silicon nanorings and silicon nanodisk mixing. Figure S15. Color palette achieved by silicon nanorings and silicon nanodisk mixing. (a) Scanning electron microscope (SEM) image of a typical silicon nanoring array. (b) Optical microscope image of the color palette as captured by 10 objective lens (NA=0.30). D varies from 80 nm to 180 nm, and g varies from 30 nm to 110 nm. The schematic shows the design of the nanoring color pixel. (c) SEM image of a typical color pixel made by silicon nanodisk S18
mixing. (d) Optical microscope image of color palette obtained by silicon nanodisk color mixing. The schematic presents the pixel design using color mixing. (e) CIE plot for the colors obtained from the silicon nanodisks from Fig. 1f, silicon nanorings from Fig. S15b and nanodisk with color mixing from Fig. S15d. S19
S16. Color matching functions for the calculation of CIE chromaticity diagram. Figure S16. Color matching functions for Blue, Green and Red colors. To convert the experimentally measured spectra from the color pixels to their CIE coordinates, the tristimulus X, Y and Z values were obtained by calculating their overlap integral with the color matching functions:, (1), (2). (3) Here, S(λ) is the measured spectrum, x(λ), y(λ) and z(λ) are the red, green and blue color matching functions as shown above. The X and Y values were then normalized to obtain the CIE (x,y) coordinates:, (4). (5) S20
S17. Multipolar decomposition technique. We study the different modes being excited in the silicon nanostructures by decomposing the polarization currents within the particles:, (6) in different multipoles. Here, is the angular frequency of the wave, the permittivity of vacuum. and denote the relative permittivities of the surrounding medium and the particle, respectively. denotes the electric field. Moreover, a complete description of the radiation properties of an arbitrary system, consisting of charges and currents in terms of its internal structure, requires the inclusion of toroidal moments, which are called the mean-square radii of the corresponding dipole distributions. 2 To be more specific, these physical quantities could be expressed with the Cartesian basis as the following:, (7), (8) 2, (9) and the mean-square radii of the dipole distributions are:, (10) 3 2, (11) where only the magnetic and toroidal components are considered, since the electric one does not contribute to radiation. 2 For the quadrupolar moments we have the following expressions: +, (12) +, (13) 4 5 + +2, (14) S21
where represents the usual dyadic product. References (1) Nieto-Vesperinas, M.; Gomez-Medina, R.; Saenz, J. J. J. Opt. Soc. Am. A 2011, 28, 54-60. (2) Radescu, E. E.; Vaman, G. Phys. Rev. E 2002, 65, 046609. S22