Open Access
Add to BibSonomyAbstract
We fabricated reflection color filters of the three primary colors with wide viewing angles using silicon two-dimensional subwavelength gratings on the same quartz substrate. The grating periods were 400, 340, and 300 nm for red, green, and blue filters, respectively. All of the color filters had the same grating thickness of 100 nm, which enabled simple fabrication of a color filter array. Reflected colors from the red, green, and blue filters under s-polarized white-light irradiation appeared in the respective colors at incident angles from 0 to 50°. By rigorous coupled-wave analysis, the dimensions of each color filter were designed, and the calculated reflectivity was compared with the measured reflectivity.
© 2014 Optical Society of America
1. Introduction
Subwavelength gratings (SWGs), which have smaller periods than the wavelengths of incident light, do not generate higher diffraction orders. When an SWG on a planar waveguide satisfies a guided-mode-resonant (GMR) condition caused by a strong coupling between modes of the incident wavelength and the periodic structure, it works as a high-efficiency band-stop filter at a resonant wavelength [1–17], which is applicable to a color filter.
Band-stop filters based on GMR conditions with both narrow and broad bandwidths have already been investigated using silicon as the SWG material because of its advanced and widespread application. For instance, Brundrett et al. theoretically investigated a narrowband filter with a bandwidth of approximately 2 nm using a silicon-on-sapphire substrate [1]. Mateus et al. experimentally demonstrated high reflectivity (> 98.5%) in a wide spectrum range (500 nm) using a poly-silicon grating [2].
Reflective color filters that produce the three primary colors (red, green, and blue) are important optical components used in reflective displays including reflective liquid crystal displays and electronic papers, charge-coupled devices (CCDs) with complementary color filters, and optical filters such as reflective dichroic color filters. Conventionally, pigments have been used as the material of color filters.
Color filters fabricated using silicon SWGs have a high degree of compatibility with light-emitting devices and CCDs based on silicon microfabrication technologies, compared with color filters using pigments. Kanamori et al. demonstrated for the first time color filters with the three primary colors of red, green, and blue using silicon SWGs on the same substrate [3]. However, these were transmission color filters and one-dimensional SWGs with polarization dependence. Recently, Cho et al. reported reflection color filters consisting of silicon two-dimensional SWGs with square-lattice patterns that produced the three primary colors [4]. However, the color filters had different heights: the red and green filters had a height of 120 nm and the blue filter had a height of 100 nm. Therefore, it is difficult to fabricate SWGs with the three primary colors on the same substrate by a single patterning process. Kanamori et al. recently demonstrated reflection color filters that produced the three primary colors using silicon two-dimensional hexagonal-lattice SWGs on the same quartz substrate. All of the color filters had the same grating thickness of 100 nm, which is ultrathin and enabled simple fabrication of a color filter array [5]. However, the optical characteristics depended strongly on incident angles. As high-angular-tolerant color filters, Cheong et al. fabricated a reflective green filter based on a two-dimensional SWG consisting of polycrystalline silicon [6]. As far as we know, there has been no experimental demonstration of high-angular-tolerant reflection color filters of the three primary colors having the same thicknesses using silicon SWGs, which are important from a practical perspective.
In order to design color filters using silicon SWGs, consideration of optical dispersion and optical interference is required in addition to the GMR condition that mainly controls the optical characteristics. The optical dispersion of silicon varies widely over the visible range. The optical interference, caused by the top and bottom boundaries of an SWG layer, appears prominently in the case of high effective-refractive-index layers such as silicon SWGs. Therefore, it is difficult to find appropriate conditions to produce the three primary colors using silicon SWGs with the same thicknesses even at normal incidence. Furthermore, when the incident angle varies, both the GMR and optical interference conditions are changed. Thus, it stands to reason that optical spectra are tuned widely depending on incident angles. Actually, Uddin et al. realized tunable color filters by means of change in incident angles [7]. For the reason mentioned above, it seems to be considerably difficult to find high-angular-tolerant conditions in addition to the above appropriate conditions.
In this paper, we fabricate reflection color filters of the three primary colors with wide viewing angles using silicon two-dimensional SWGs on the same quartz substrate. All of the color filters have the same grating thickness of 100 nm, enabling simple fabrication of a color filter array. Because the incident angle dependency of the reflectance spectra is different depending on the SWG structures for respective color filters, it is not surprising that there has been no experimental report on high-angular-tolerant reflection color filters of the three primary colors using silicon SWGs. The key ideas for designing color filters with wide viewing angles are summarized in the following two points. First, although the reflectance spectrum of each color filter changes according to incident angles, each color filter appears in the same color at wide viewing angles if the hue does not change in different hues within the wide range of incident angles. Therefore, we designed color filters to fall within respective hues within the wide range of incident angles. Second, when the effective refractive indices of SWG layers become higher, the bandwidth of resonant wavelengths that corresponds to a photonic band gap becomes wider and also angular tolerance becomes higher due to stronger optical couplings. Therefore, we used silicon with high refractive index as material of SWGs. Reflectivity at the visible spectrum domain is measured and compared with numerical values obtained by rigorous coupled-wave analysis (RCWA), which yields accurate results using Maxwell’s equations in the frequency domain [18–24].
2. Design
Two types of SWG arrangements to obtain color filters with wide viewing angles were designed: square- and hexagonal-lattice SWGs. Both arrangements have rotational symmetry without polarization dependency of normal incident light. Figures 1(a) and 1(b) show schematics of color filters with square- and hexagonal-lattice SWGs, respectively. Each color filter has a two-dimensional SWG with a period Λ, a diameter a, and a thickness of 100 nm, which is formed on a quartz substrate with a thickness of 800 μm. The material of the SWG is single crystalline silicon. An SWG groove and the surrounding media are composed of air. For great enough filling factor of the material, the effective refractive index of an SWG layer is higher than its surrounding, and the SWG layer functions as a planar waveguide and satisfies the GMR condition. A reflected light generates only a zeroth diffraction order because Λ satisfies the SWG condition. SWG design was performed using commercial software (DiffractMOD, Synopsys, Inc.) based on the RCWA technique that has been implemented using advanced algorithms. Material dispersions of silicon [25] and quartz [26] are included in RCWA. The order of the Fourier coefficients used in the calculation was between the −4th and + 4th order for each x and y direction. The two-dimensional SWGs shown in Fig. 1 consist of circular disks that are similar to the fabricated structures shown in Fig. 5, although treatment of the circular boundary in RCWA is not a trivial task. An adequate SWG arrangement for each color filter was selected from the two types of SWG arrangements. SWG thickness of 100 nm was determined by experimental reasons and was not an optimized value, that is, a silicon layer thickness of obtainable silicon-on-quartz (SOQ) substrates. The SWG thickness of 100 nm is a suitable value. In the case of SWG thickness larger than several hundred nanometers that produces a multimode in the GMR structure, multiple reflectance peaks across different hues are generated. In the case of SWG thickness being smaller than tens of nanometers, on the other hand, a resonant peak disappears due to weak coupling efficiency. Figure 1(c) depicts the configuration of incident light. At an incident angle of 0°, the incident light is s-polarized and irradiated along the direction normal to the substrate surface. The s-polarized incident light is a state in which the component of the electric field is normal to the plane of incidence. In this paper, azimuth angle, which is an angle measured from the x-axis in the xy-plane in spherical coordinates, was fixed to 0°, and p-polarized incident light was not considered. The p-polarized incident light is a state in which the component of the electric field is parallel to the plane of incidence. Investigations of the optical characteristics for the azimuth angle and the p-polarized incident light are necessary for intended device application, and they are topics of future study.
Fig. 1 Schematics of (a) a square-lattice SWG, (b) a hexagonal-lattice SWG, and (c) incident light configuration. Λ and a are the period and diameter of the SWGs, respectively. θ and E are the incident angle and electric field of the incident light, respectively.
Reflectivity was calculated at normal incidence in order to design each period of red, green, and blue filters. Figures 2(a)-2(c) show the calculated reflectivity of the SWGs as functions of Λ and wavelength at normal incidence for a/Λ = 0.45, 0.40, and 0.40 and the lattices of square, square, and hexagonal, respectively. It is found that the resonant wavelengths are proportional to Λ. Furthermore, with an increase in a/Λ, the optical coupling under the GMR condition becomes stronger, and a higher reflectance and a wider bandwidth are obtained at GMR wavelengths. In the case of a/Λ being larger than a certain value that produced a multimode in the GMR structure, however, multiple reflectance peaks across different hues were generated. Then appropriate values for Λ and a were chosen for each filter in consideration of fabrication difficulty. Designed periods of Λ = 400, 340, and 300 nm for red, green, and blue filters, respectively, are indicated by white dotted lines in Figs. 2(a)-2(c). The SWGs are designed conclusively to be Λ of 400, 340, and 300 nm, a/Λ of 0.45, 0.40, and 0.40, and lattices of square, square, and hexagonal, for red, green, and blue filters, respectively. All of the SWGs have the same thickness of 100 nm. The dependence of resonant wavelength and width of the peak at GMR conditions with respect to the parameters of the SWG structures has been identified in previous works [15, 16].
Fig. 2 Calculated reflectivity as functions of wavelength and period at normal incidence in order to design each period of (a) red, (b) green, and (c) blue filters for a/Λ of 0.45, 0.40, and 0.40 and lattices of square, square, and hexagonal, respectively.
Figures 3(a)-3(c) show the calculated reflectivity of the designed red, green, and blue filters, respectively, as functions of incident angle and wavelength. As can be seen, all of the calculated color filters have wide viewing angles between 0 and 50° for s-polarized incident light.
Fig. 3 Calculated reflectivity of (a) red, (b) green, and (c) blue filters as functions of wavelength and incident angle.
3. Fabrication
Figure 4 shows schematics of the fabrication steps. First, an electron-beam (EB) resist (ZEON ZEP520A-7) with a thickness of 155 nm is spin-coated at 7000 rpm for 60 s on an SOQ substrate, which consists of a 100-nm-thick crystalline silicon layer on an 800-μm-thick quartz substrate [Fig. 4(a)]. After the resist coating, a water-soluble electroconductive solution is coated onto the EB resist to prevent charging up during EB writing [Fig. 4(b)]. Next, SWG patterns are drawn by EB lithography (JEOL JBX5000LSS) [Fig. 4(c)]. For the patterning, the acceleration voltage was 50 keV and the beam current was 100 pA. After the EB drawing, the water-soluble electroconductive solution was removed by dipping the sample in water. After development, using the patterned EB resist as a mask, the silicon layer is etched by a fast atom beam (EBARA FAB-60ML) of SF6 gas [27]. As the parameters of fast atom beam etching, a gas flow rate of 5.6 sccm, an accelerating voltage of 2.5 kV, and a coil current of 20 mA were used. The etching depth was controlled by the etching time. The etching rate of silicon was 14.6 nm/min. Finally, the residual EB resist is removed by O2 plasma ashing [Fig. 4(d)].
Figures 5(a)-5(c) show scanning electron microscopy (SEM) photographs of top views of the fabricated SWGs for red, green, and blue filters, respectively. Silicon circular patterns are arrayed with square-, square-, and hexagonal-lattices for red, green, and blue filters, respectively, as designed. All of the SWGs are fabricated successfully with periods Λ of 400, 340, and 300 nm, mean diameters a of 185, 151, and 136 nm, and a/Λ of 0.46, 0.44, and 0.45 for red, green, and blue filters, respectively, with a thickness of 100 nm. Fabricated SWG periods are in agreement with the designed values for all of the color filters. However, SWG diameters differ between the designed values and fabricated values. We believe that the difference results from fabrication errors caused by an overdose of electron beams in the lithography process in addition to degradation of a mask pattern in the fast atom beam etching process.
Fig. 5 SEM photographs of fabricated SWGs for (a) red (Λ = 400 nm, a = 185 nm), (b) green (Λ = 340 nm, a = 151 nm), and (c) blue (Λ = 300 nm, a = 136 nm) filters.
4. Optical characteristics
Figure 6 shows reflected colors of the fabricated red, green, and blue filters under s-polarized white-light irradiation at θ = 0, 10, 30, and 50°. Each SWG has a 280 × 280 μm2 rectangular area. A three-CCD camera (TOSHIBA JK-TU53H) was used as a color camera to obtain micrographs with high color reproducibility. Each fabricated filter produces a uniform color in the SWG area as shown in Fig. 6. If the period or shape of the fabricated SWG is partially disturbed within the area of the color filter, it is expected that the produced color is also partially varied depending on them. As can be seen in Fig. 6, the hues of reflected colors from red, green, and blue filters fall within respective hues at incident angles from 0 to 50°.
Fig. 6 Reflected colors of the fabricated SWGs under s-polarized white-light irradiation at θ = 0, 10, 30, and 50°.
Reflection spectra at incident angles between 10 and 50° were measured with a home-built measurement system for variable-angle reflectance measurement in microscopic regions. Figures 7(a) and 7(b) show a picture and an optical diagram of the measurement system, respectively. A tungsten halogen light source (LS-1, Ocean Optics, Inc.) is used as a light source of the incident light. In order to irradiate the incident beam within the fabricated SWG area, light emitted from an optical fiber with a core diameter dcore of 50 μm on an irradiation side is focused on the SWG surface by two lenses and polarized by a polarizer. The focused beam on the SWG surface has a circular cross-section with a diameter of 150 μm at a normal direction and has elliptical cross-sections at slant incidence conditions. Reflected light from the SWG is gathered with two lenses and propagated into an optical fiber with dcore of 400 μm on a receiver side. Then the light is received by a spectroscope (HR2000, Ocean Optics, Inc.). The irradiated incident beam on the SWG surface is observed by a CCD with a zoom lens. Fabricated SWGs are put on an xyz-stage. The xy-stage is used for alignment between the positions of the incident beam and the SWG area. The z-stage is used for focusing of the incident beam on the SWG surface. A lens and polarizer unit on the irradiation side and a lensunit on the receiver side are mounted on rotating motors and their rotation angles of θi and θr (θi = θr in this measurement), respectively, are controlled independently with a motor controller between the angles of 7 and 90°. An aluminum mirror was used as a reference to estimate reflectivity of the fabricated SWGs. Focal lengths of lenses 1 and 2 shown in Fig. 7(b) are 10 and 30 mm, respectively. Collimated light between the lens 1 and lens 2 has 4 mm in diameter. On the other hand, reflection spectra at normal direction were measured with a microspectroscope system, which consisted of a microscope combined with a spectroscope. Normal incident light from a tungsten halogen light source (LS-1, Ocean Optics, Inc.) was focused on the SWGs by an objective lens. Reflected light from the SWGs was collimated by the objective lens and then passed through a polarizer. Polarized light passing through the polarizer was coupled to an optical fiber and then received with a spectroscope (HR2000, Ocean Optics, Inc.).
Fig. 7 (a) A picture and (b) an optical diagram of a home-built measurement system for variable-angle reflectance measurement in microscopic regions.
Figure 8 shows measured and calculated reflectivity as a function of wavelength at θ = 0, 10, 30, and 50°. Figures 8(a)-8(c) show the measured spectra for red, green, and blue filters, respectively. Figures 8(d)-8(f) show the calculated spectra for red, green, and blue filters, respectively. The results shown in Figs. 6 and 8 were obtained under the same incident light. All of the measured spectra, especially those at resonant wavelengths, almost agree with the calculated values. It is noteworthy that even though the incident angles are changed from 0 to 30°, there is almost no shift in the peak wavelength for each color filter as explained by the calculation shown in Figs. 3 and 8(d)-8(f). For the blue filter, measured spectra have roughly two peaks at wavelengths around 520 and 430 nm as the first and second peaks, respectively.
Although the first peak falls within a green hue, the fabricated blue filter appears in blue color because the second peak falls within a blue hue, and furthermore the reflectivity at wavelengths longer than 550 nm including green and red hues is suppressed. Maximum reflectivity of 81% is experimentally obtained at a wavelength of 620.84 nm and the incident angle of 0° for the red filter. Even at θ = 50°, all color filters experimentally yield maximum reflectivity of more than 50%. Degradation of the measured optical characteristics is caused by fabrication errors, resulting in scattering loss, such as those caused by minute fluctuations in the diameter, surface roughness, and shape of SWGs. As another possible reason, experimental situations with the finite size of the SWG area and the finite size of the incident beam caused discrepancy between the calculated values and the measured values because the RCWA calculations were performed using an infinite periodic structure and a plane wave for the incident wave.
5. Conclusion
We have fabricated for the first time reflection color filters of the three primary colors with wide viewing angles using silicon two-dimensional SWGs on the same quartz substrate. In the fabrication, EB lithography and fast atom beam etching of SF6 gas were used. All of the SWGs were fabricated successfully with periods of 400, 340, and 300 nm and mean diameters of 185, 151, and 136 nm for red, green, and blue filters, respectively, with a thickness of 100 nm. Hues of reflected colors from the red, green, and blue filters fell within respective hues at incident angles from 0 to 50° under s-polarized white-light irradiation. Reflectivity of the fabricated filters was measured for the visible spectrum domain. Maximum reflectivity of 81% was experimentally obtained at a wavelength of 620.84 nm and incident angle of 0° for the red filter. Even at θ = 50°, it was experimentally shown that all color filters yielded maximum reflectivity of more than 50%. Numerical calculations, especially at resonant wavelengths, using RCWA explained the measured results well.
Acknowledgments
A Part of this work was supported by MEXT KAKENHI 25109702 and 25120503, and was performed in the Micro/Nano-Machining Research and Education Center in Tohoku University, Japan.
References and links
1. D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Normal-incidence guided-mode resonant grating filters: design and experimental demonstration,” Opt. Lett. 23(9), 700–702 (1998). [CrossRef] [PubMed]
2. C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004). [CrossRef]
3. Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Photon. Technol. Lett. 18(20), 2126–2128 (2006). [CrossRef]
4. E.-H. Cho, H.-S. Kim, B.-H. Cheong, O. Prudnikov, W. Xianyua, J.-S. Sohn, D.-J. Ma, H.-Y. Choi, N.-C. Park, and Y.-P. Park, “Two-dimensional photonic crystal color filter development,” Opt. Express 17(10), 8621–8629 (2009). [CrossRef] [PubMed]
5. Y. Kanamori, T. Ozaki, and K. Hane, “Fabrication of ultrathin color filters for three primary colors using guided-mode resonance in silicon subwavelength gratings,” Opt. Rev. 21(5), 723–727 (2014). [CrossRef]
6. B.-H. Cheong, O. N. Prudnikov, E. Cho, H.-S. Kim, J. Yu, Y.-S. Cho, H.-Y. Choi, and S. T. Shin, “High angular tolerant color filter using subwavelength grating,” Appl. Phys. Lett. 94(21), 213104 (2009). [CrossRef]
7. M. J. Uddin and R. Magnusson, “Efficient guided-mode-resonant tunable color filters,” Photon. Technol. Lett. 24(17), 1552–1554 (2012). [CrossRef]
8. S. Tibuleac and R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14(7), 1617–1626 (1997). [CrossRef]
9. Y. Kanamori, T. Kitani, and K. Hane, “Guided-mode resonant grating filter fabricated on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 45(3A), 1883–1885 (2006). [CrossRef]
10. T. Katchalski, E. Teitelbaum, and A. A. Friesem, “Towards ultranarrow bandwidth polymer-based resonant grating waveguide structures,” Appl. Phys. Lett. 84(4), 472–474 (2004). [CrossRef]
11. Y. Kanamori, H. Katsube, T. Furuta, S. Hasegawa, and K. Hane, “Design and fabrication of structural color filters with polymer-based guided-mode resonant gratings by nanoimprint lithography,” Jpn. J. Appl. Phys. 48(6), 06FH04 (2009). [CrossRef]
12. R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992). [CrossRef]
13. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993). [CrossRef] [PubMed]
14. G. Niederer, H. P. Herzig, J. Shamir, H. Thiele, M. Schnieper, and C. Zschokke, “Tunable, oblique incidence resonant grating filter for telecommunications,” Appl. Opt. 43(8), 1683–1694 (2004). [CrossRef] [PubMed]
15. D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997). [CrossRef]
16. F. Lemarchand, A. Sentenac, E. Cambril, and H. Giovannini, “Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1(4), 545–551 (1999). [CrossRef]
17. Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, and R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett. 23(19), 1556–1558 (1998). [CrossRef] [PubMed]
18. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995). [CrossRef]
19. P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13(4), 779–784 (1996). [CrossRef]
20. G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13(5), 1019–1023 (1996). [CrossRef]
21. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13(9), 1870–1876 (1996). [CrossRef]
22. E. Popov and M. Nevière, “Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18(11), 2886–2894 (2001). [CrossRef] [PubMed]
23. T. Schuster, J. Ruoff, N. Kerwien, S. Rafler, and W. Osten, “Normal vector method for convergence improvement using the RCWA for crossed gratings,” J. Opt. Soc. Am. A 24(9), 2880–2890 (2007). [CrossRef] [PubMed]
24. T. Weiss, G. Granet, N. A. Gippius, S. G. Tikhodeev, and H. Giessen, “Matched coordinates and adaptive spatial resolution in the Fourier modal method,” Opt. Express 17(10), 8051–8061 (2009). [CrossRef] [PubMed]
25. D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press, 1985).
26. H. R. Philipp, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press, 1985).
27. Y. Toma, M. Hatakeyama, K. Ichiki, H. Huang, K. Yamauchi, K. Watanabe, and T. Kato, “Fast atom beam etching of glass materials with contact and non-contact masks,” Jpn. J. Appl. Phys. 36(12B12B), 7655–7659 (1997). [CrossRef]
