Description of the transparent resonant NW arrays

When designing detectors for the visible spectral range, it is important to realize that the lowest-lying resonance frequencies for NWs are observed for transverse magnetic (TM) polarization with the electric field along the NW axis. As a result, the optical response for small-diameter Si NWs (e.g. 10–100 nm) is dominated by the TM response and the transverse electric (TE) resonances are conveniently shifted towards the ultraviolet. Figure 1b illustrates this point for an array of rectangular cross-sectional Si NWs that have a width w = 55 nm, a height h = 110 nm, and are spaced at a period p = 280 nm to achieve strong absorption in the green. Based on the dominance of the TM response, we first optimized the red, green, and blue detector arrays for this polarization state. Figure 1c shows that arrays with nicely overlapping, but shifted absorption spectra can be realized.

In order to understand the symmetry properties of the resonances supported by rectangular NWs, it is helpful to view them as Fabry–Pérot-style resonators in which light can oscillate in either the horizontal or vertical direction35. An approximate resonance condition for the different-order resonances can be written as

$$n_{{\mathrm{Si}}}^2\left( {2{\mathrm{\pi }}/\lambda } \right)^2 = \left( {m{\mathrm{\pi }}/w} \right)^2 + (n{\mathrm{\pi }}/h)^2,$$ (1)

where n Si is the refractive index of Si and m, n count the number of antinodes in the dominant field component along the horizontal and vertical directions. We find that the first-order TM resonance exhibits a symmetric field profile in the vertical direction, while the second-order resonance is anti-symmetric with two antinodes, as shown in the insets to Fig. 1h. From Eq. (1) it is clear that for single NWs the optical resonances with opposite symmetry are naturally occurring at different frequencies (blue curve in Fig. 1h). In contrast to single nanoparticles, single NWs intrinsically do not support degenerate even and odd resonances for any cross-sectional geometry (Supplementary Fig. 1). The directional scattering recently observed in a single NW33 is the result of the Kerker condition with two spectrally misaligned resonances. Therefore, single NWs show strong backscattering at other wavelengths and cannot be used for color detection (no single-peaked absorption spectrum).

Next, we illustrate how degenerate even and odd resonances can be engineered in a NW array by tailoring the radiative coupling between them. To highlight the basic physics, we first analyze a single Si NW in air and assume a constant index of 4 for the Si material. Its first-order resonant mode features an even symmetry. It has an omnidirectional radiation pattern and a very low quality factor (Q~1) that results from efficient far-field radiation. In an array of these Si NWs, the in-plane radiation gives rise to the formation of a new resonant mode with a scattering spectrum that is notably blueshifted from the original, single NW resonance. The solid red line in Fig. 1h shows the scattering spectrum for an array with a 280 nm period. An analysis of the field distribution at λ = 500 nm, near the resonance peak, indicates that this can be viewed as a different type of Fabry–Pérot-style resonance where light oscillates back and forth between neighboring NWs. As a result, the associated resonance frequency is controlled by the NW spacing (inset to Fig. 1h and Supplementary Fig. 2). This resonant mode maintains the even symmetry seen for the single NW resonance, but features a higher Q. The second-order mode of a single NW features the desired odd symmetry that is needed to cancel backreflections. Due to its higher quality factor (Q~10) and out-of-plane, vertical radiation pattern, the coupling between NWs is negligible for this resonance. As a result, its spectral location remains the same in the array (see Fig. 1h). The first-order (even) and second-order (odd) resonances can thus be shifted independently, enabling the creation of NW arrays with degenerate optical resonances at any wavelength in the visible range.

Based on this insight, we first tune the even and odd resonances to a target wavelength of 550 nm and fabricate the resulting geometry in an Si film on a transparent sapphire substrate by electron-beam lithography. Simulations show a single, broad scattering resonance that is peaked around 550 nm (green line in Fig. 1i), attributed to the two degenerate optical resonances. The scattering from the NW array shows a giant asymmetric distribution with almost no backscattering (red, blue lines in Fig. 1i), which is also corroborated by the scattering field distributions (inset to Fig. 1i). For this subwavelength NW array, there are no allowed diffracted orders and the scattered light is forced into the forward direction. Using a multipole decomposition of the simulated full-fields of the NW array36,37,38, we verify the mode degeneracy (Supplementary Fig. 3). A similar NW array with a non-optimized, near-unity aspect ratio (Fig. 1f) is also fabricated next to the optimized array (Fig. 1g) for comparison. Figure 1e shows the reflection optical image of the NW arrays with the word “Stanford” written underneath. The reflected light was filtered for the targeted resonance wavelength and polarization (TM polarization, center wavelength 550 nm, FWHM = 32 nm) to highlight the feature induced by degenerate resonances. For the engineered NW array, light is first transmitted through the NW array, reflected by the word “Stanford”, and finally transmitted back through the NW array. The clear visibility of the logo confirms the transparency induced by the degenerate resonances. On the other hand, for the non-optimized NW array with non-degenerate resonances, strong backscattering from the NWs prevents us from seeing anything behind the array. A more detailed comparison between the “conventional” and “transparent” NW arrays is summarized in Supplementary Fig. 4.

Experimental demonstration of transparent detection pixels

Using the approach described above, we also design and fabricate transparent NW arrays with degenerate optical resonances at the wavelengths of 485 nm (blue) and 625 nm (red), as described in Supplementary Fig. 5. Unlike degenerate optical resonances in nanodisks—which require a fixed aspect ratio and thus different heights for different resonance wavelengths—NW arrays can be made transparent at different wavelengths in the visible using a fixed height of 110 nm. This facilitates multiplexing of different types of transparent pixels in a single patterning step. The simulated reflection of these designed NW arrays is less than 1% at the designed wavelengths for TM-polarized illumination (Supplementary Fig. 6). We measure the reflection (Fig. 2a) and transmission (Fig. 2b) spectra for TM polarization of the three different NW arrays in a confocal optical microscope and achieve good agreement with the simulated results. For example, the minimum reflection observed is 3.5% around 625 nm for the “red” pixel, clearly lower than the reflection from the bare sapphire substrate, and with a transmission/reflection ratio of 25. The small wiggle observed around 600 nm in the transmission spectrum for “red” pixel is due to the excitation of a guided mode resonance, which can be excited at off-normal incidence or with the gently focused light used here39,40 (Supplementary Fig. 7).

Fig. 2 Transparency of fabricated NW array pixels. a Reflectance and b transmittance as a function of wavelength for three different NW array pixels designed for red (w = 110 nm, p = 310 nm), green (w = 55 nm, p = 280 nm), and blue (w = 30 nm, p = 230 nm) light for both polarizations. The inverted triangles indicate the wavelengths at which the NW pixels show zero reflectance in the simulations. The reflectance and transmittance of the substrate (black) is also included for reference and the reflection from the back surface of the sapphire substrate is removed in post data-processing. Insets: a Reflection and b transmission optical images for “green” pixels for two orthogonal polarizations. The incident light is polarized in the vertical direction and the NWs are aligned in the vertical direction for the left pixel and in the horizontal direction for the right pixel, respectively. A green color filter was used. Scale bar: 25 μm. c Overall white-balanced transmittance of three different NW array pixels as a function of wavelength for both polarizations. Insets: Transmission optical images of 25 μm size (top), 5 μm size (bottom left), and 2 μm size (bottom right) NW array pixels under TM-polarized illumination. Scale bar: 10 μm (top) and 5 μm (bottom). d Optical reflection images of multiplexed 5-μm-size NW array pixels under unpolarized white-light top illumination. Different colored letters “S” are placed under the pixel array. Scale bar: 25 μm Full size image

To assess the performance of this detection platform for randomly polarized light, it is also important to analyze the case of TE-polarized illumination. Interestingly, the anisotropic NW array can function as a good antireflection (AR) coating for both polarizations. For TE polarization, all optical resonances exist in the ultraviolet spectral range, except the first-order resonance for “red” pixels (Supplementary Figs. 8 and 9). This resonance results in a non-perfect AR behavior, but does not prevent the use of the NW arrays for spectro-polarimetry. For the cases that the NW array is off-resonance, its effective index can simply be estimated using first-order effective medium theory (ε eff = ε air ε Si /(f air ε Si + f Si ε air )). The resulting effective refractive index (n eff,b = 1.07, n eff,g = 1.11, n eff,r = 1.22) is near the geometric mean of the indices of air and sapphire (n g = 1.33), affording good antireflection behavior. The AR behavior for both polarizations can be seen from an analysis of the reflection and transmission spectra as well as the reflection and transmission optical images of two “green” arrays with orthogonal NW orientations (Fig. 2a, b and insets). The optical images were taken with linearly polarized light through a broadband green color filter (center wavelength = 550 nm, FWHM = 32 nm). These results indicate that the proposed NW array could be used as a transparent spectrally selective and polarization-sensitive detector.

Figure 2c shows the averaged transmission spectrum measured from 25-μm-sized “red”, “green”, and “blue” pixels (top insets in Fig. 2c). Transmission optical images of two multiplexed NW arrays with pixel sizes of 5 μm (bottom left) and 2 μm (bottom right) are also shown in Fig. 2c. The consistency of the pixel color at different multiplexing dimensions indicates that the NW array detector can be scaled down to sub-10 μm, comparable to color filter arrays used in commercial digital cameras. Keeping in mind that the typical transmittance for sun glasses is around 20% as a reference, the observed white-balanced transmission spectrum with a designed ~70% overall transmittance for both polarizations opens up the opportunity for in situ detection process under day-light illumination. If a lower transmittance is acceptable, NW arrays that offer an increased photocurrent can be realized. In order to visualize the transparency of the multiplexed NW arrays, we place objects with different colors under the multiplexed NW pixel array and take reflection optical images under unpolarized white-light illumination (Fig. 2d). All the objects with colors from blue to red can be clearly recognized, verifying the good transparency for practical applications.

Color and polarization detection

Next, we apply two aluminum contacts at the ends of the NW arrays to form transparent Al–Si–Al photodetectors. Besides detection of the light intensity, our transparent photodetectors also extract color and linear polarization information of the incident light by the carefully tuned resonant nature of the Si NWs. We apply a small external voltage (1 V) to drift the photo-generated free carriers to the metal contact pads and collect them. Assuming the internal quantum efficiency (IQE) is wavelength-independent in the visible range, the external quantum efficiency (EQE) becomes linearly dependent on the absorption efficiency η abs of the array (EQE = IQE × η abs ). We verify that the spectral dependence of the measured EQE spectra taken from the three NW array detectors agrees well with the simulated absorption spectra (Supplementary Fig. 9). Due to the resonantly enhanced absorption, the designed NW arrays absorb red, green, and blue light separately. This affords color detection analogous to conventional Si diodes with RGB color filters, or the three types of light-sensitive cone cells in human eyes. Unlike our ultrathin transparent detector, traditional photodiodes with color filter arrays and cone cells are micrometer thick and non-transparent. Analogous to the well-established 1931 Commission International de Eclairage (CIE) chromaticity diagram, we can define a color space using the extracted photocurrent value from three photodetectors as tristimulus values41,42. Figure 3a shows the outline of this color space calculated from the measured EQE and simulated absorption ratio of three transparent photodetectors under TM-polarized monochromatic illumination between 460 nm and 700 nm. The measured EQE ratio agrees very well with the simulated absorption ratio and the outline shape of the generated color space traces a wide trajectory in the CIE diagram (Supplementary Fig. 10), justifying the color detection ability. Since TM polarization dominates the optical absorption, the color detection also works well for unpolarized incident light (Fig. 3b), which is essential for many practical applications. Moreover, for each color pixel, the strong polarization-dependent Mie resonance naturally enables polarization detection within each color band, as shown in Fig. 3c. The photocurrent ratio between two adjoined photodetectors with orthogonal NW orientation is dictated by the polarization of the incident light.

Fig. 3 Color and polarization detection and uniform photocurrent generation. a The color space defined by the extracted photocurrent value from three fabricated NW array photodetectors for TM-polarized and b for unpolarized illumination. The dashed back line shows the simulated absorption ratio as a function of wavelength between 450 and 700 nm. The colored dots show the measured EQE ratio from 460 to 700 nm in steps of 10 nm. The x-axis is defined as I R /(I R + I G + I B ) and y-axis is defined as I G /(I R + I G + I B ). For monochromatic illumination, the photocurrent ratio is equivalent to the absorption ratio and the EQE ratio. Insets: Reflection optical images (top) and reflection maps (bottom) of three NW photodetectors. The reflection maps are taken at 625, 550, and 485 nm, respectively. Scale bar: 20 μm. c Measured “green” pixel EQE as a function of wavelength for two orthogonal polarizations. Inset: Measured photocurrent at 550 nm as a function of the angle between the incident polarization and the NW orientation. d Schematic of a Si/ITO interdigitated NW array photodetector. Photocurrent is extracted transversely across the Si NWs. e Electric field distribution and the power flow lines of the proposed Si/ITO interdigitated photodetectors under normal incidence. f False-color cross-section SEM image of the as-fabricated interdigitated Si/ITO NW array photodetector. Scale bar: 100 nm. g Normalized photocurrent map of the interdigitated NW array photodetector (inset: photocurrent map for bare Si NW array photodetector. Scale bar: 20 μm) at a wavelength of 625 nm for TM polarization. The black (white) dashed box shows the position of the Si/ITO interdigitated (Si) NW array detector. h Normalized EQE of Si/ITO interdigitated NW array detector (red) and bare Si NW array detector (black) as a function of the position along the NWs for x = 0. Two dashed red (black) lines indicate the Si/ITO interdigitated NW array detector (Si NW array detector) area Full size image

Some of the known challenges with NW-array detectors are related to increased carrier recombination and a reduced charge extraction efficiency as compared to bulk detectors43. Also in our devices, the highest photocurrents are produced near the electrical contacts (inset in Fig. 3g). This is primarily caused by the short and different diffusion lengths for electrons and holes in these etched Si NW arrays. Here, we show how we can maintain a high transparency of our detectors while promoting a more uniform photocurrent generation by applying indium-tin-oxide (ITO) interdigitated electrodes, as illustrated in Fig. 3d. Two sets of transparent electrodes with opposite DC polarity are interdigitated between the Si NWs. The 20-nm-thick ITO electrodes introduce negligible changes to the optical properties of the Si NW array (transparency and strong absorption per unit volume), because most of the power flows through the Si NWs without the interaction with ITO electrodes (Fig. 3e, Supplementary Figs. 11–13). At the same time, the photo-excited charge carriers are extracted transversely across the NWs such that free-carrier diffusion distance decreases notably from tens of micrometers to tens of nanometers. Figure 3f shows a cross-sectional SEM image of the as-fabricated device. Robust contact areas between ITO electrodes and Si NWs can be observed, with exactly the same geometry as illustrated in Fig. 3e. A spatially resolved photocurrent map at resonance is shown in Fig. 3g. The EQE signal uniformity is greatly enhanced with only 15% signal fluctuation over 80% of the device area (red lines in Fig. 3h). Unlike the exponentially decaying photocurrent generation along the bare Si NWs (black lines in Fig. 3h), the Si/ITO interdigitated detector displays quasi-uniform photocurrent generation area in the middle part of the detector. It enables a reliable intensity detection process for practical applications.