We demonstrate the design and fabrication of a highly efficient guided-mode resonant color filter array. The device is designed using numerical methods based on rigorous coupled-wave analysis and is patterned using UV-laser interferometric lithography. It consists of a 60-nm-thick subwavelength silicon nitride grating along with a 105-nm-thick homogeneous silicon nitride waveguide on a glass substrate. The fabricated device exhibits blue, green, and red color response for grating periods of 274, 327, and 369 nm, respectively. The pixels have a spectral bandwidth of ~12 nm with efficiencies of 94%, 96%, and 99% at the center wavelength of blue, green, and red color filter, respectively. These are higher efficiencies than reported in the literature previously.
© 2013 OSA
Electronic devices such as televisions, computers, mobile phones, digital cameras, e-readers, and multimedia projectors contain various color filters for image display. The liquid crystal display (LCD) is a dominant technology primarily using dye-based color filters, which transmit a particular color under white light illumination . Limitations include low efficiency, heating due to light absorption, and imperfect color selectivity. The class of grating-based color filters [2–12] is an interesting alternative, potentially overcoming these limitations on account of high efficiency and improved band selection. Feasible grating materials include semiconductors (silicon) [2,3], metals (aluminum) [4–7], dielectrics (nitride/oxide) [8–10], or polymers .
Displays can be transmissive, reflective, or transflective. In transmissive displays, an internal light source is required whereas reflective displays can work with ambient light; transflective displays use both internal and external light sources to augment low ambient light levels. Transmissive displays often apply silicon and aluminum with attendant low efficiency [2–7] due to high absorption in the visible spectrum region. Well-known transmissive displays are LCD televisions and computer monitors. Reflective display technologies may be based on grating light-valves , digital micro-mirror devices , and interferometric modulators . These displays use micro-electro-mechanical systems-based control of the pixels. In reflective displays under ambient light, the color filters must be highly efficient to reflect most of the light. We define efficiency as the ratio of the intensity of the reflected output light to the intensity of the input light at a particular wavelength, which is also known as reflectance. Dielectric guided-mode resonance (GMR) reflective filters can have high efficiency with reasonably narrow bandwidth [16,17], favorably impacting input light utilization and color purity. Recently, we reported an angle-tuned highly efficient color filter  for projection display applications. Prior to that, Wang et al.  provided computed results of a reflection-type color filter array using photoresist material based on the GMR principle; Kanamori et al.  reported a polymer-based reflection color filter array (CFA) with experimental efficiency of 50%. Cho et al.  reported an a-Si-based reflection CFA with experimental efficiency of 30% for the blue, 75% for the green, and 85% for the red color filter.
In this paper, we report the design results and fabrication of a GMR-based CFA using subwavelength silicon nitride (Si3N4) gratings on a glass substrate. We design and optimize the filter parameters using numerical methods based on rigorous coupled-wave analysis . We fabricate the filters using laser interferometric lithography for patterning. We realize three pixels on the same substrate with differing periods and attendant resonance wavelengths. We report efficiency exceeding 94% at the center wavelength of the fabricated blue, green, and red color filters. A dielectric reflective CFA with comparable experimental efficiency has not been reported previously. The color filters developed in this research show improved input light utilization due to higher efficiency and higher color purity due to narrower bandwidth. The CFA can be incorporated with existing reflective LCD display technology to produce colored displays. It may also find use in reflective projection display technology.
2. Theory and design
The color filter array under consideration consists of a subwavelength silicon nitride grating along with a silicon nitride homogeneous waveguide layer on a glass substrate. The device layers and parameters are shown in Fig. 1 , where dg denotes grating depth, dh homogeneous waveguide thickness, F fill factor, Λ period, I incident light wave, T0 zero-order transmittance, and R0 zero-order reflectance. A GMR takes place when diffracted light from the grating structure couples with a leaky waveguide mode satisfying the phase-matching condition; a resulting sharp resonance peak with 100% reflectance is observed at a particular wavelength. GMR filter operation details are explained in . We set the grating period to be significantly smaller than the wavelengths in the visible range, which allows the device to work in the zero-order diffraction regime. The dimensions of the gratings such as grating grooves and periods are optimized to achieve particular (RGB) resonance wavelengths and attendant lower sidebands for the unwanted part of the spectrum. The position of the resonance wavelength can be tuned by changing the refractive index, period, thickness, and incident angle as discussed in [16,17].
In this paper, we use different grating periods of the GMR filter, keeping other device parameters constant to obtain three primary colors. The device possesses a symmetric grating profile exhibiting a single resonance under normal incidence. We design the device using numerical methods based on rigorous coupled wave analysis . To achieve optimal reflectance, we adjust the device parameters including period, grating depth, and waveguide thickness. The optimized design parameters for all pixels are dg = 55 nm, dh = 110 nm, and F = 0.5. The optimized periods of the device are 275 nm for the blue, 325 nm for the green, and 375 nm for the red color. Computed reflectance of the designed CFA for the normally incident transverse-electric (TE) polarized light is given in Fig. 2 . The center wavelengths for blue, green, and red pixels are 484 nm, 555 nm, and 626 nm, respectively, with full width half maximum of ≈10 nm. We use the wavelength-dependent dispersive optical constants of Si3N4 as shown in Fig. 3 for the design of the filters.
Using the reflectance of the color filters, the displayable red, green, and blue primary colors can be calculated using standard equations as provided in . The first step is to calculate the Commission Internationale de l’Eclairage (CIE) XYZ tristimulus values of a color as expressed by,
here,, and are CIE 1931 standard observer color-matching functions, D(λ) is the energy distribution of the illuminant, and we use CIE normalized illuminant D65 that closely matches the characteristics of daylight. For convenience we use a fourth-order polynomial approximation of this function; p is the normalizing coefficient that can be obtained using Eq. (2), which is defined in such a way that an object with a uniform unity reflectance will have the Y component of the tristimulus value equal to unity.
Then, a linear matrix multiplication is performed using Eq. (3) to calculate the intermediate linear RGB colors. The numerical values used for the conversion matrix match those specified in the IEC 61966-2-1: 1999 standard.
Thereafter, using Eq. (4) below, these linear RGB values are converted into standard RGB components (sRGB). In Eq. (4), a = 0.055, Csrgb represents Rsrgb, Gsrgb, or Bsrgb, and Clinear represents Rlinear, Glinear, or Blinear. Finally, the values of Csrgb are changed to the 8-bit range of 0 to 255 by multiplying it with 255 and rounding off to the closest integer. The perceived color then can be constructed from the integer Csrgb values.
3. Device fabrication and characterization
Device fabrication starts with Si3N4 thin-film deposition on a clean microscopic glass substrate using a sputtering system. The optical constants and thickness of the film are measured using ellipsometry. The film thickness is 165 nm and the measured optical constants for the Si3N4 film in the visible spectral region are given in Fig. 3.
Thereafter, a 300-nm-thick positive photoresist (PR) is spin coated at 2000 rpm on Si3N4. The adhesion of PR with Si3N4 is not very strong. To increase the adhesion, a very thin hexamethyldisiloxane (HMDS) layer is spin coated at 3000 rpm on Si3N4 film before applying the photoresist. HMDS crosslinks PR with Si3N4 and increases the adhesion. The HMDS is baked at 120°C for 120 seconds, and the PR is baked at 110°C for 90 seconds. Then a 1D grating pattern is recorded on the PR using a laser interferometric lithography system. Our laser interferometric lithography system is based on a classic Lloyd-mirror geometry with a pattern period conveniently controlled by a simple stage rotation. The exposing laser has a 266-nm wavelength; it is well polarized and provides up to 200 mW output power in a very narrow spectral band. The exposed PR is developed for 50 seconds in AZ 917 MIF developer followed by DI water rinsing for 60 seconds. To etch the nitride film, we use reactive ion etching (RIE) involving a gas mixture of trifluromethane (CHF3) and oxygen (O2). We run a short 10-s descum recipe using O2 plasma before the etching step to ensure no PR remains at the bottom of PR pattern. After RIE, a thin PR film still exists on the nitride grating and it is stripped using O2 plasma. Finally, we use wet cleaning with nanostrip (90% H2SO4 and 5% H2O2) followed by O2 plasma ashing to ensure that no PR remains on the nitride grating. Figure 4 shows a clear summary of the steps used to fabricate the CFA.
The device is characterized using an atomic force microscope (AFM). From the AFM image, we verify the period, grating thickness, and fill factor. The waveguide thickness is calculated by subtracting the grating thickness from the film thickness, which is measured by ellipsometry. The AFM image in Fig. 5 shows the grating profile of the blue pixel. From the AFM image and ellipsometric data, the fabricated device parameters are dg ≈58.5 nm, dh ≈106.5 nm, Λ ≈274 nm, and F ≈0.46. Figure 6 shows the grating profile of the green pixel; the fabricated device parameters are dg ≈59.2 nm, dh ≈105.8 nm, Λ ≈327 nm, and F ≈0.46. Figure 7 shows the grating profile of the red pixel; the fabricated device parameters are dg ≈60.5 nm, dh ≈104.5 nm, Λ ≈369 nm, and F ≈0.46. We see that for devices with larger periods, the grating depth is a bit larger than that of the lower period devices. This phenomenon is known as the macroscopic loading effect . For higher periods, due to the larger opening area, a higher density of gases reacts with the material to be etched. This creates a larger grating depth for devices with larger periods even though the etch time is the same.
The fabricated devices have an approximate grating thickness of 60 nm and a waveguide thickness of 105 nm, which are close to the initial design parameters (grating thickness of 55 nm and waveguide thickness of 110 nm). The periods (274 nm, 327 nm, and 369 nm) of the fabricated pixels are also close to the initial design parameters (275 nm, 325 nm, and 375 nm).
The effective pixel size can be calculated using the decay length of the leaky waveguide mode. The decay length is approximately Ld ≈Λλ/4πΔλ, where Δλ is the spectral linewidth of the color filter . Using this equation, we estimate the decay length as ~2 μm. Thus, this pixel should work well with, for example, 10 × 10 μm2 lateral dimensions, which significantly exceed this decay limit. The fabricated pixels presented here are considerably larger (5 × 5 mm2) for convenience in characterization and spectral measurements. Fabricated device dimensions can be reduced subsequently to ~10-μm scale devices using, for example, smaller apertures in the laser interferometric lithography system.
4. Results and discussion
The reflectance or efficiency as a function of wavelength of the fabricated color filters is measured using a spectrum analyzer. A tungsten halogen lamp with a wavelength range of 360–2000 nm serves as the light source. A polarizer is mounted in front of the light source to select a specific polarization state. We use normally incident TE polarized light in which the electric field vector is normal to the plane of incidence and along the grating grooves in Fig. 1. At first, we measure the reflected light intensity as a function of wavelength from a reference mirror. Then, we measure the reflected light intensity from the color filter. The computer stores these data in separate files. Then, we calculate the reflectance of the color filter by taking the ratio of reflected intensity from the sample to the reflected intensity from the reference mirror for each wavelength.
Figure 8 shows the reflectance of the fabricated blue, green, and red pixels. For the blue pixel, efficiency is 93.7% at the center wavelength of 479.5 nm; for the green pixel, efficiency is 95.9% at the center wavelength of 551 nm; for the red pixel, efficiency is 99.6% at the center wavelength of 607 nm. The measured full width at half maximum or spectral width is ~12 nm. The pixels have the same grating thickness, homogeneous layer waveguide thickness, and fill factor, but three different grating periods, as shown in Fig. 8 to reflect the three primary colors.
Figure 9 compares the experimental, simulated, and fitted reflectances of the fabricated blue pixel. The simulated reflectance is calculated using the device parameters found by AFM and ellipsometry measurements. To fit the reflectance data, we slightly adjust the device parameters to take into account the measurement errors in AFM and ellipsometry so that the calculated and experimental curves match more closely. The fabricated device parameters are Λ = 273.15 nm, dg = 58.5 nm, F = 0.46, and dh = 106.5 nm and these same parameters are used for simulation; the parameters for fitted curve are Λ = 276 nm, dg = 58.5 nm, F = 0.46, and dh = 106.5 nm.
Figure 10 compares the experimental, simulated, and fitted reflectances of the fabricated green pixel. The fabricated device parameters are Λ = 327 nm, dg = 59.2 nm, F = 0.46, and dh = 105.8 nm and these same parameters are used for simulation; the parameters for fitted curve are Λ = 323.5 nm, dg = 59.2 nm, F = 0.46, and dh = 105.8 nm.
Figure 11 compares the experimental, simulated, and fitted reflectances of the fabricated red pixel. The fabricated device parameters are Λ = 369 nm, dg = 60.5 nm, F = 0.46, and dh = 104.5 nm and these same parameters are used for simulation; the parameters for fitted curve are Λ = 363.6 nm, dg = 60.5 nm, F = 0.46, and dh = 104.5 nm.
Table 1 summarizes the measured and fitted device parameters used in Figs. 9–11. All the device parameters except the periods are kept same. Adjusting the device periods by a few nanometers provides the appropriate fitting of the experimental results, with the exception of the slight deviation in the sidebands.
From the experimental reflectance values, standard RGB components (sRGB) values are calculated using Eqs. (1)–(4). The sRGB values are 90, 98, and 154 for the blue pixels; 92, 148, and 82 for the green pixels; and 162, 83, and 82 for the red pixels. Figure 12 shows the perceived colors using the sRGB values of the pixels found from the experimentally observed reflectance values of the pixels.
A highly efficient GMR-based reflective CFA is designed and fabricated using a subwavelength Si3N4 grating along with a homogeneous Si3N4 layer on a glass substrate. The array separates incident TE-polarized white light into its three primary colors: red, green, and blue. It exhibits high efficiency ~95% as well as high color purity due to the narrow bandwidth of ~12 nm. We find a good match between the experimental data and theoretical simulation results. The device has potential for applications in compact reflective LCD display and generally in projection display technology.
This research was supported in part by the UT System Texas Nanoelectronics Research Superiority Award funded by the State of Texas Emerging Technology Fund. Additional support was provided by the Texas Instrument Distinguished University Chair in Nanoelectronics endowment. The authors thank Jae Woong Yoon and Tanzina Khaleque for their help during this work.
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