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Abstract
Advances in augmented reality and virtual reality platforms have sparked interest in high-performance metasurface color filters with elevated resolution, saturation, and durability. However, the predominant use of either dielectrics or metals prevents the realization of efficient “transmissive” color filters for displays. Here, we propose a novel, to our knowledge, approach combining dielectric and metallic components, optimizing complex structures using inverse design with height restrictions on the layers of red, green, and blue. The optimized structure achieved full coverage of the sRGB color space and surpassed 70% efficiency. Experimental validation demonstrated the potential of the inverse design for enhancing the performance of complex structures.
© 2023 Optica Publishing Group
1. INTRODUCTION
Artificial color implementation has predominantly relied on two approaches: chemical pigments and structural colors [1–4]. Conventional optical filters used in cameras and visual displays have been based primarily on chemically synthesized colors. However, such chemical dyes have been found to be environmentally harmful. Moreover, their limitations in the form of low resolution, low saturation, and low CMOS compatibility necessitate the development of high-performance color filters, particularly in the context of augmented reality and virtual reality platforms. Structural colors have garnered significant attention as a means of resolving these limitations [5–8]. Inspired by nature, structural colors are created using nanostructures that interact with visible light. They offer numerous advantages, including high resolution, durability, environmental friendliness, and the ability to change colors based on structural variations of subwavelength-scale thickness [9,10].
Metasurfaces can be used to control emitted light by using two-dimensional arrays of subwavelength artificial structures. These structures, often referred to as meta-atoms, have emerged as innovative alternatives to traditional optical elements. Following advances in nanofabrication and design methods [11–15], these structures have been extensively studied with respect to various ultra-compact optical applications, such as holographic displays [16–20], metalenses [21–25], absorbers [26–28], detecting devices [29–32], and structural color filters [33–35]. Metasurface-driven color filters can meet the growing demand for extremely high pixel densities in future display applications owing to their submicrometer scales. In the case of structural color achieved through metasurfaces with dielectric substrates, two main materials are used in the unit cell structure: dielectrics and metals. When dielectrics are used to create colors, electric dipole (ED) and magnetic dipole (MD) (or higher-level multipole) interactions are employed with Mie resonance and lattice resistance [36–39]. Alternatively, when metals are used to create colors, a collective oscillation of an electric field and light (called a surface plasmon) is utilized at the interface between the metal and dielectric [40–43]. This allows for filtering specific wavelengths into reflective and transmissive modes while inducing surface plasmon resonance (SPR) at incident light with specific wavelengths and incident angles. SPR-based design of optical materials is a major research topic at present.
However, current research has not extensively explored the production of high-efficiency and high-color-purity transmission colors by using both dielectric and plasmonic color filters, notwithstanding the significant demand for displays. Dielectric color filters have primarily been studied in the context of reflective outcoupling, reinforced through ED and MD interactions by Mie resonance and lattice resistance, resulting in structures that predominantly reflect a specific wavelength. Consequently, transparent color filters using dielectrics have focused on implementing subtractive colors, such as magenta, cyan, and yellow. As evident from the Commission on Illumination (CIE) 1931 color diagram, such subtractive colors cannot accommodate a wide color spectrum, making them unsuitable for display purposes [44–46]. Efforts have been made to implement additive colors such as red, green, and blue using transmission-type dielectric structures. This approach appears to be fundamentally limited to selectively transmitting specific visible colors of light when using dielectrics, which inherently transmit all colors of light [47,48]. However, attempts to implement transparent color filters using nanoholes and grating structures for plasmonic color filters have been hindered by reduced efficiencies owing to ohmic losses in metals [9,40,43,49].
In this study, we designed high-performance transmission structures utilizing dielectric and metal components for displays, achieving high saturation and high efficiency. These structures possess the advantages of straightforward manufacturability, polarization independence, and a large field of view (FoV) [50]. In such dielectric–metal hybrid structures, the metal passes a specific wavelength through SPR, and the dielectric breaks the symmetry and enhances the efficiency [51,52]. Straightforward fabrication of our material was achieved through height unification and aspect ratio limitations of each structure (with respect to red, green, and blue). To consider both the complexity and fabrication feasibility of the structure, we chose an inverse design analyzed through simulation instead of modeling.
2. RESULTS AND DISCUSSION
A. Computational Simulation and Optimization
Figure 1 illustrates the schematic and design procedure for the entire structure. To achieve wide color-space coverage in the CIE 1931 chromaticity diagram, we utilized a hybrid metasurface that combined metal and dielectric components. The objective was to design a high-saturated transmissive metacolor filter for display applications that required design constraints originating from the fabrication process and light source [53]. We designed three types of color filters, corresponding to red, green, and blue, respectively. Uniform dielectric and metal layer heights are required because of the color variation based on the pixel arrangement on a single glass substrate [54]. Additionally, for effective compatibility with commonly used light-emitting diode sources [55], polarization independence is essential [56]. The design process generally involves several design parameters and constraints, making it impractical to determine the optimal structure through a manual search or parameter sweep methods. Consequently, in this study, we developed a simulation and optimization platform tailored to solve these challenges in a metacolor filter design based on particle swarm optimization (PSO), a global optimization technique. PSO is an effective algorithm for simple problems compared to other optimization algorithms such as deep-learning-based methods. It does not require large amounts of data, computational power, or many internal parameters to be set [57]. Using this platform, we devised a metacolor filter capable of exhibiting high color saturation while ensuring efficient light transmission.
Fig. 1. Schematic of the optimized transmission-type color filter. (a) Schematic of metasurfaces with both metal and dielectric components. The aluminum (Al) is located on top of the silicon nitride (${{\rm Si}_3}{{\rm N}_4}$) layer. In consideration of practical display usage, the heights of both dielectric and metal structures are fixed to have identical dimensions of red, green, and blue colors, aiming to optimize ease of fabrication and production cost. (b) Schematic of color filter optimization. Unit cells are created with design parameters, which are simulated spectrum characteristics using FDTD. Both the permeability of the unit cell and the area that can be covered by the CIE color space are considered, and the structure is optimized using the PSO technique.
Typically, when simulating periodic nano-optical structures, a finite-difference time-domain (FDTD) method [58], a finite element method [59], or a rigorous coupled-wave analysis (RCWA) [60] are commonly used to solve Maxwell’s equations. However, simulating metallic materials using RCWA requires a high Fourier number, which leads to increased computational costs and limits the practicality of optimization. Therefore, in this study, we simulated a metasurface that combined metal and dielectric materials using an FDTD solver (Ansys Lumerical). Additionally, to integrate the optimization codes, we developed an optimization module in Python and utilized the Lumerical-Python API to obtain the FDTD results within the Python environment [61]. In this design, we needed to optimize seven or eight design parameters for the final design, while simultaneously considering various constraints. To address this challenge, we employed PSO to determine the optimal design. Three types of metasurfaces were implemented based on the given design parameters, and their respective spectral information was obtained through FDTD simulations after passing through the structures. Subsequently, the spectral information was transformed into the corresponding $x - y$ coordinates on the 1931 CIE diagram. Considering both high transmittance and wide color space area as important criteria, we introduced a new figure of merit (FoM) for evaluation:
A PSO process involves particles, each of which contains information regarding the design parameters and corresponding values of the FoM. Through iterative processes, the particles update their sequential sets of parameters by combining three terms of the 8D vectors, as shown in Eq. (2):
During each iteration, if the new design parameters violate the given boundary conditions, have excessively high aspect ratios, or result in impractical structures (period < structure size), a damping boundary condition is applied to recreate the particles that comply with the constraints [63]. Subsequently, simulations are performed using the revised particles. To resolve the convergence limitations caused by particle regeneration and the high dimensionality of the design parameters, we introduced an internal design parameter control method into the standard PSO process. This approach dynamically adjusted the coefficients of the three terms in the PSO iteration, allowing for improved optimization, as shown in Eq. (3) [64]:
where $v_i^t$ is the velocity vector of the $i$th particle in the $t$th iteration, and $P_i^t$ is the position of the $i$th particle in the $t$th iteration. The first, second, and final terms on the right-hand side of Eq. (2) are the inertial, local minimum, and global minimum terms, respectively. $w$, ${c_1}$, and ${c_2}$ are the inertial, personal, and global coefficients, respectively. The coefficients are determined by equations that are dependent on the number of iterations $t$ and particle number $n$, as expressed in Eqs. (3a)–(3c). The coefficient of the local minimum term was set to decrease with the number of iterations, whereas that of the global minimum term was set to increase with the number of iterations.When designing the color filters using only dielectric materials, seven design parameters were optimized, including the period (${{\rm P}_{\rm{cyan}}}$) and gap (${{\rm G}_{\rm{cyan}}}$) of the cyan (630 nm) target meta-atom, period (${{\rm P}_{\rm{magenta}}}$) and gap (${{\rm G}_{\rm{magenta}}}$) of the magenta (532 nm) target, and period (${{\rm P}_{\rm{yellow}}}$) and gap (${{\rm G}_{\rm{yellow}}}$) of the yellow (430 nm) target, and height of the dielectric material (${{\rm H}_{\rm{dieletric}}}$). Detailed results are shown in Fig. 2(a) [38]. Owing to the limitations of subtractive colors, it is challenging to expect high saturation from the red, green, and blue colors used directly in displays. Therefore, their complements—cyan, magenta, and yellow—may be targeted for optimization. In order to achieve a higher FoM, we set the FoM to increase as the combined transmission intensity of red (635 nm), green (532 nm), and blue (430 nm) light decreased [Fig. 2(b)]. To prevent the length from exceeding the periodicity of the structure during iterations, we utilized the gap between the structures (instead of the width) as a variable. This ensured that the period and size of the structures were different, while maintaining the same height. In the final design, we created square ${{\rm Si}_3}{{\rm N}_4}$ structures on a glass surface, as shown in Fig. 2. Although all the structures had the same height, their periods and dimensions differed from one another.
Fig. 2. Simulations and optimization results for the dielectric-based color filter. (a) Optimized dielectric-based transmissive color filters (${\rm Height} = {380}\;{\rm nm}$, ${{\rm Period}_{\rm red}} = \;{582}\;{\rm nm}$, ${{\rm Gap}_{\rm red}} = \;{338}\;{\rm nm}$, ${{\rm Period}_{\rm{green}}} = {500}\;{\rm nm}$, ${{\rm Gap}_{\rm{green}}} = {215}\;{\rm nm}$, ${{\rm Period}_{\rm{blue}}} = {422}\;{\rm nm}$, ${{\rm Gap}_{\rm blue}} = \;{220}\;{\rm nm}$). (b) Transmission spectra for the cyan, magenta, and yellow filters. Each spectrum displays suppression of the intensity of the target complementary color: red (635 nm), green (532 nm), and blue (430 nm). (c) Distribution in the CIE 1931 color space.
Fig. 3. Simulations and optimization results for the dielectric–metal hybrid color filter. (a) Optimized dielectric–metal hybrid transmissive color filter (${{\rm H}_{\rm{metal}}} = {50}\;{\rm nm}$, ${{\rm H}_{\rm{dielectic}}} = {145}\;{\rm nm}$, ${{\rm Period}_{\rm{red}}} = {400}\;{\rm nm}$, ${{\rm Gap}_{\rm{red}}} = {60}\;{\rm nm}$, ${{\rm Period}_{\rm{green}}} = {336}\;{\rm nm}$, ${{\rm Gap}_{\rm{green}}} = {91}\;{\rm nm}$, ${{\rm Period}_{\rm{blue}}} = {283}\;{\rm nm}$, ${{\rm Gap}_{\rm{blue}}} = {96}\;{\rm nm}$). (b) CIE 1931 color space compared the simulation result and ideal (DCI-P3) space. Since the area within DCI-P3 is essential among the color spaces of the designed structures, only the overlapping parts with the DCI-P3 area were used when calculating the cover area for the FoM. (c) Transmission spectra for the red, green, and blue color filters. Each color filter emphasizes the peak intensity (red: 630 nm, green: 532 nm, blue: 430 nm) as well as increasing the cover space area. (d) Oblique incidence sweep result. As the incident angle increases, the same color can be implemented, but the intensity of the peak decreases, leading to lower saturation.
Dielectric-based color filters pose a challenge for utilization in display color filters because they can only implement subtractive colors, as shown in Fig. 2(b). Therefore, we induced surface plasmons through a metallic film layer to increase the transmissivity and focused ED, electric quadrupole, MD, and magnetic quadrupole at the desired target wavelength, successfully achieving a narrow full width at half-maximum (FWHM). Compared to previous methods, adding metal height as a design variable resulted in using eight parameters. Owing to constraints on the achievable thickness of the metal layer in the fabrication process, the appropriate height of the metal layer was found to be in the range of 10–100 nm. Although the heights of the metal layer and dielectric were identical, we designed three types of color filters with different periods and gaps. As a result of the optimization, we determined the height of each dielectric and metal layer, and the period and gap for each color structure [Fig. 3(a)]. We were able to obtain a high saturated color spectrum compared with using only dielectrics. It was possible to fully cover the sRGB region and 75% of the DCI-P3 color space, which is widely used for evaluating display color filter performance. The FWHM values were 40 nm for red, 46 nm for green, and 41 nm for blue, outperforming the existing transmissive color filters [Fig. 3(c)]. Because only square structures on the X–Y plane were used, the performance was polarization-independent. The size of the FoV is crucial for using a device as a display color filter. Therefore, we computationally proved that our device was able to maintain 50% peak transmission up to an angle of incidence of 20 deg, as shown in Fig. 3(d).
Fig. 4. Schematic of the fabrication process and optical measurement setup. (a) Proposed metal–dielectric hybrid color filter fabrication process using electron beam lithography. (b) Customized measurement apparatus for the characterization of fabricated transmissive color filters.
B. Experimental Verification
To fabricate our metal–dielectric hybrid transmissive color filters, we adopted the conventional nanofabrication process using electron beam lithography (EBL) and dry etching [Fig. 4(a)]. First, a 145-nm-thick layer of ${{\rm Si}_3}{{\rm N}_4}$ was deposited using a plasma-enhanced chemical vapor deposition system (BMR Technology HiDep-SC) on a cleaned fused silica (${{\rm SiO}_2}$) substrate. A single layer of positive-tone photoresist (Microchem, 495 PMMA A6) was then applied using a spin coater at 4000 rpm. We used EBL (ELIONIX, ELS-7800) to expose the color filter patterns onto the resist, and the exposed photoresist was cold-developed in a methyl isobutyl ketone/isopropyl alcohol 1:3 solution for 11 min 30 s. Using the developed color filter patterns, we deposited a 90-nm-thick aluminum (Al) layer using electron beam evaporation (KVT, KVE-ENS4004) to form a hard mask and structure. After the lift-off process, dry etching (TEL, Dry Etcher) was conducted to etch ${{\rm Si}_3}{{\rm N}_4}$ and Al. Because of the high etch selectivity of Al for ${{\rm Si}_3}{\rm N4}$, the remaining Al height after dry etching was approximately 50 nm, which agreed well with our metasurface-based color filter design. Our fabrication method followed conventional metasurface fabrication but was simpler than the traditional method because no process was required to remove the leftover hard mask at the end. We used a customized optical measurement setup to measure the transmission spectrum and color space [Fig. 4(b)]. By integrating a commercial optical microscope system (Olympus, IX70) and a spectrometer (HORIBA, iHR320), stable white light was transmitted through our metasurface color filters. The transmitted light was focused onto an objective lens (Olympus, LMPlanFL50X) to magnify the images. The focused light was transferred to the spectrometer, and the spectrum and color space of the light were analyzed. Apertures were used in the optical setup to increase the measurement accuracy.
Figure 5 illustrates the measured and simulated transmission spectra of the optimized structure that achieved the widest coverage in the CIE 1931 color space [65]. A trade-off between color saturation, cost-effectiveness, and ease of fabrication was encountered while keeping the heights of the blue, green, and red structures fixed. Nevertheless, as evident in Fig. 5(a), it was possible to implement a simulated color coverage area that exceeded the sRGB gamut by 104%. The color coverage area based on the color coordinates from the experimental results was smaller than that of the sRGB gamut. Experiment results only can cover the 46% of sRGB. This discrepancy between the simulated and experimental results in the color coordinates was attributed to fabrication errors. The SEM image of an actual fabricated sample is presented in Fig. 5(b), confirming the occurrence of fabrication errors, such as tapering, or deviations from the intended dimensions at increased heights.
Fig. 5. Optimized transmission color for the widest coverage in the CIE color space. (a) CIE 1931 chromaticity coordinates for simulated (“o” shaped dot) and measured (“x” shaped dot) spectra. (b) Corresponding SEM images of the blue, green, and red structures. The color enclosing the SEM image represents the SEM image of the structure. (c) Simulated (solid line) and measured (dashed line) spectra of the optimized structure. The insets in the upper right corner of each spectrum are simulated (solid line) and measured (dashed line) color.
Notwithstanding these process errors, as demonstrated in Fig. 5(c), the simulated (solid line) and measured (dashed line) spectra exhibit similar results. Considering transmission during optimization, the average maximum transmission in the simulation for the blue, green, and red channels was 0.69, with individual values of 0.78, 0.72, and 0.57, respectively. Similarly, in the actual measurements, the average maximum transmission was 0.70, with values of 0.65, 0.83, and 0.63 for the blue, green, and red channels, respectively. This indicates that the designed and measured transmissive colors ensured stable high transmittance and color purity.
3. CONCLUSION
We successfully optimized and experimentally demonstrated transmissive metasurface color filters tailored for displays with high saturation efficiency and resolution. Through optimization, we resolved the challenge of achieving high-quality additive colors when using dielectrics alone by adopting a comprehensive approach incorporating dielectric and metal components. The inherent directionality of specific-color light owing to the plasmonic surface resonance of metals initially caused a uniform distribution in both the reflective and transmissive directions, resulting in a transmittance efficiency of 0.5 or lower in the transparent direction. However, by introducing asymmetry in the structure using dielectrics, we effectively harnessed light transmission, significantly enhancing the efficiency. Furthermore, we employed an inverse design methodology to optimize the complex structures, striving for wide color coverage and heightened efficiency while emphasizing practical fabrication for real-world display applications. This led us to impose height constraints on the dielectric and metal components of the red, green, and blue structures. As a result of these collective interventions, the optimized structure achieved complete coverage of the sRGB color space and a transmittance efficiency exceeding 70%. Experimental validation demonstrated the performance levels of the optimized structure. The demonstrated potential of the inverse design for achieving high performance with intricate structures is expected to serve as an asset in the pursuit of advanced functionalities of color filters such as tunable color [66–68].
Funding
Korea Institute of Industrial Technology (KITECH EO-22-0005); LG Display (C2022008004); National Research Foundation of Korea (NRF-2022M3C1A3081312).
Acknowledgment
The authors thank Dr. Jungho Mun (POSTECH) for providing the RCWA codes.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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