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Design of CMOS anti-Hermitian metasurface

The color-sorting metasurface is composed of three types of silicon nanocylinders with different diameters d, patterned into a hexagonal lattice with a sub-wavelength center-to-center nanocylinder spacing, a, of 220 nm, as illustrated in Fig. 1a. From Mie theory, silicon nanoparticles can support strong magnetic dipole resonances in the visible spectral range13,14,15,16. Here, the sizes of the three types of nanocylinders are optimized to achieve selective absorption in the red (dR = 136 nm), yellow (dY = 122 nm) and green (dG = 104 nm) part of the visible spectrum, respectively (herein denoted [dRdYdG] = [136 122 104] nm). The silicon nanocylinders are doped into vertical p-i-n junctions, and a thin transparent layer of indium tin oxide (ITO) is sputtered on top as electrical contact, shown schematically in Fig. 1b. The neighboring nanocylinders are electrically isolated from one another by the air gap between the intrinsic and n-doped regions, resulting in negligible electrical crosstalk.

Fig. 1: Optical design and simulation of three-channel, two-dimensional, anti-Hermitian PIN Si metasurface.

a Top- and b side-view schematic of 3-color, 2-D array of silicon nanocylinders. c, e Simulated absorption spectra of normally incident light in green-, yellow-, and red-absorbing nanocylinders for lattice constants of c 350 nm, mixed coupling condition, and e 220 nm, anti-Hermitian coupling condition. d, f Simulated dissipated power in each nanocylinder at the associated wavelength of peak absorption (590, 610, and 640 nm in d and 575, 590, and 625 nm in f). It can be seen that when the lattice constant is above the anti-Hermitian regime, the three-color spectra are broad and overlapping, leading to optical color crosstalk between three-color channels. The optimal structure designed by the principle of anti-Hermitian coupling has enhanced quality factors, leading to a significant reduction of color crosstalk and improvement of the peak absorption efficiency. Source data for c and e are available in the Source Data File tabs labeled 1c and e, respectively.

While the optical coupling coefficient κij is generally a complex number, the AH condition is achieved by carefully choosing the separation distance between nanocylinders, such that the real part from the direct and indirect coupling cancel each other, resulting in sharpened resonances and reduced optical crosstalk (Supplementary Note 1). The real and imaginary coupling constants between yellow-absorbing and green-absorbing nanocylinders, and yellow-absorbing and red-absorbing nanocylinders, are shown in Supplementary Fig. 1a–f, respectively, as a function of the center-to-center separation distance, a, for three different scaling factors of the nanocylinder diameters.

When a = 350 nm, far from the AH condition, broad, overlapping absorption spectra are observed, which leads to relatively low peak absorption values as well as color crosstalk if these nanocylinders were to be used as pixels (Fig. 1c, d). By contrast, Fig. 1e, f shows the simulated absorption spectra and dissipated power of the same nanocylinders with a = 220 nm, which corresponds to an optimized AH condition with consideration of fabrication constraints. It can be clearly seen that selective chromatic absorption is achieved at three distinct colors with small overlapping. The peak absorption efficiencies reach 30%, owing to the large absorption cross-section of the silicon nanocylinders. Because the derivate of the coupling constants with respect to the separation distance is relatively small (Supplementary Fig. 1), small deviations as ‘near-anti-Hermitian’ from the optimal geometry are expected to also yield good performance in terms of peak absorption and low crosstalk. Simulation results of metasurfaces with varying scale factors, shown in Supplementary Fig. 2, verify this expectation, thus permitting deviations from ideal designs based on constraints associated with fabrication of the nanocylinder array.  After being optimized for their optical response, simulations of photocurrent generation in the nanocylinders, shown in Supplementary Fig. 3, confirmed their viability for efficient photodiode operation. 

Fabrication of CMOS anti-Hermitian metasurface

Conversion of optical energy into electrical photocurrents with minimal crosstalk requires well-controlled fabrication of 130-nm-thick poly-Si layer vertical p-i-n junction and accurate control of nanocylinders’ diameter and center-to-center distance in a hexagonal lattice.  A schematic of the complete device is shown in Fig. 2. The p-i-n junction prepared in this work is successively laminated, forming p-type Si, intrinsic Si and n-type Si with thickness of 50–70 nm, 30–70 nm, and 10–30 nm, respectively. Contrary to previous research of color sorting using 2.7-μm-thick PIN Si rods17, AH-coupling design of 0.22 μm sub-pixels faces the challenge to create a vertical p-i-n junction of Si with a thin thickness of just 130 nm. Supplementary Figure 4 summarizes the process steps for creating the vertical shallow junction PIN Si layer devised in this study. Extinction coefficient (k) of PIN poly-Si is measured as a low value of 0.097 as well as high refractive index of 4.269 at 550 nm wavelength. Poly-Si deposition and ion implantation are applied to forming vertical p-i-n junction as a mass productive method. The complete fabrication process is summarized in “Methods” section and Supplementary Fig. 5.

Fig. 2: Device layout of CMOS color sensors based on anti-Hermitian metasurfaces.
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a Top- and b side-view of color sensor device layout including electrical contacts. c Oblique view of scanning electron micrograph, just after nano patterning of PIN Si rods. d Side cross-section view and e top view of nanocylinder array, after SiO2 gap-filling and ITO electrode deposition. The white scale bar corresponds to 500 nm in ce. The diagonal red line in c and e indicates the cross-section presented in d.

According to the design of the AH metasurface, the optimized diameters of the standard scale nanocylinders are 104, 122, and 136 nm, which correspond to green, yellow, and red sub-pixels, each with the height of 100 nm. ITO electrode, connected to Au pad (top pad), has contact with one n-type Si of three colors. P-type Si acts as an electrical common ground and is connected to another Au pad (bottom pad), as shown in Fig. 2b. 30 nm-thick SiO2 separates the upper regions of n-type Si from ITO electrode (see Supplementary Note 2 for discussion on blue part of spectrum).

Fig. 3: Experimental three-channel color-sorting in anti-Hermitian PIN Si metasurface.
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Experimental photocurrent (solid curves) and simulated absorption (dashed curves) spectra of the AH PIN Si metasurface when electrical connection is made to a green, b yellow, and c red color channels. For clarity, all curves are normalized to their peak values. d Combined photocurrent and absorption spectra of all three channels. Legend labels “sim”, “expi”, and “exp” refer to simulated, interpolated experimental, and raw experimental data, respectively. Source data for ad are provided in the Source Data File tabs labeled ac, respectively.

Experimental demonstration of high-performance color-sensing

Devices designed for AH coupling were compared to planar devices with identical PIN silicon material makeup but lacking nanostructure via etching. The device clearly exhibits diode-behavior with large forward-bias currents and small reverse-bias currents (Supplementary Fig. 6). Consistent with photodiode behavior, as the illumination power increases, the current increases for a fixed reverse-bias level, indicating that the devices show the necessary behavior for color and image sensors18. To separate the optical response of the AH devices from their electrical transport properties, reflection spectra were measured of control devices and AH devices of varying scale. Whereas the control devices exhibit a single reflection dip, as shown in Supplementary Fig. 7, each AH metasurface shows three distinct reflection minima, which are associated with absorption maxima, as shown in Supplementary Fig. 8.

With these superior optical behavior, the combined optical and electrical response was probed via photocurrent spectroscopy. Figure 3a–d shows the normalized photocurrent spectra of individually addressed devices designed to absorb red, yellow, and green light, along with the normalized simulated absorption spectra. Sharp resonances with peak wavelength and quality factors comparable to those predicted by numerical simulations are observed. Figure 4a shows the measured responsivity, defined as the ratio of photocurrent to illumination power, of the three-color channels, with values of approximately 0.35 A/W, 0.30 A/W, and 0.25 A/W for red, yellow, and green, respectively, at the bias voltage of −0.5 V and illumination power of 0.5 μW. Fixing the wavelength to 630 nm, Fig. 4b shows increasing photocurrent with illumination power, which is approximately linear over this range, indicative of proper photodiode behavior. By contrast, the photocurrent spectra of the control devices lacked any resonant character and samples with poorly designed nanocylinder spacing exhibited overlapping resonances, with significant optical crosstalk. Based on these results we confirm the observation of near-AH coupling with high responsivity in 3 visible channels in the shallow junction PIN silicon metasurface. Furthermore, photocurrent measurements of metasurfaces with varying scale factors demonstrate that the AH condition is robust to small geometric changes, as shown in Supplementary Fig. 9.

Fig. 4: Performance characteristics of CMOS color sensors based on anti-Hermitian metasurfaces.
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a Measured responsivity as a function of wavelength at reverse-bias of −0.5 V and illumination power of 0.5 μW for green, yellow, and red color channels. b Measured photocurrent as a function of reverse-bias in red color channel at illumination wavelength of 630 nm with illumination power parameterized. Source data for a and b are provided in the Source Data File tabs labeled a and b, respectively.



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