CMOS-compatible all-dielectric metalens for improving pixel photodetector arrays

Recent advances in the nanofabrication technology resulted in the enhanced interest to light manipulation with flat nanostructured components—metasurfaces.¹ Due to the high technological potential, the field of metasurfaces was booming during the last decade, resulting in a variety of design ideas and description methods. Besides, metasurfaces keep finding more and more promising applications including miniature integrated devices such as on-chip spectrometers,² camera objectives,³ compact integrated microscopes,^4,5 etc. For many of them, it is of special interest to study wavefront shaping metasurfaces, in particular, metalenses.

Currently, the main metalens designs are based on arrays of nanoparticles and can be roughly classified depending on their size with respect to the wavelength. The first class of metalens use nanoparticles in a resonant regime, which allows for controlling scattering phase varying resonators’ shape, size, placement, and composition.^6,7 The second class of metalens employs nanoparticles in an off-resonant sub-wavelength regime. In this case, the metasurface can be described with a locally varying effective refractive index, and focusing is achieved by introducing the geometric phase difference into the beam.^8–10 We further concentrate only on all-dielectric structures as they are known to demonstrate better efficiency.¹¹ One of the most efficient types of metasurfaces is the Huygen’s metasurface based on the mode interference within Mie-resonant high refractive index particles.¹² Although metasurfaces of this type were also designed for a visible domain,¹³ the operation wavelength choice is significantly limited by the lack of lossless high-index materials in this range. In addition, due to their resonant nature, these metasurfaces are narrow-band.

On the other hand, devices based on the geometric phase manipulation are advantageous for the broadband operation. The way to design them works with sub-wavelength resonators arranged in a particular way. In the case of devices based on a Berry phase,^14–17 resonators are anisotropic and the phase gradient is introduced by rotating them at a different angle. These metalenses operate only with circularly polarized light, which, however, was shown to be beneficial for broadband imaging applications. For the design of polarization-independent components, resonators are chosen to be symmetric and vary only in size. Although such metasurfaces are described using different formalisms, such as light propagation in fundamental-mode waveguides,^18,19 scattering on sub-wavelength diffraction grating,^20–22 or gradient index (GRIN) surfaces,^23,24 they are all subject to homogenization and can be described with effective parameters (in the case of the Berry phase, the anisotropic effective refractive index is used, and in other cases, the gradient refractive index is used). Most of the suggested options of graded-index metasurfaces are designed with high aspect ratio dielectric posts, which require a complex fabrication process.^14,15,19 In addition, most materials used before are not CMOS-compatible, such as titanium oxide or PMMA, which means that the component cannot be readily integrated into the more complex device.

Here, we develop, fabricate, and characterize a flat metalens design featuring several key advantages. It is fully CMOS-compatible and requires only simple nanostructuring of the surface. The optical performance combines an excellent transmission with focusing on a submicron size spot. Moreover, our metalens is polarization-insensitive, operates over a large spectral bandwidth, and appears to be quite robust to nanofabrication deficiencies. While a similar design was recently introduced in the far infrared region of the spectrum where the fabrication is much easier,²⁵ here, it is the first time that this approach is demonstrated in the visible spectral range. Our general design can be easily implemented on a large range of applications, notably to improve the photodetection efficiency (PDE) of photodetector arrays, for example, of silicon photomultipliers which are increasingly used as photodetectors in many applications. Focusing the light onto the active region of a photodetector pixel is an efficient approach to reduce the negative impact of the limited fill factor (FF) and improve the photogenerated signal. We focus on a simple design based on the hyperbolic secant profile,^23,25,26 which is one of the perfectly imaging index profiles derived from the Maxwell fish-eye distribution with transformation optics methods.²⁷ Our metalens design is suitable for many CMOS-compatible fabrication methods and accessible materials. In this work, it is produced with a fabrication process consisting of e-beam vapor deposition and Focused Ion Beam (FIB) milling using the niobium pentoxide Nb₂O₅ material,²⁸ which has a large transparency window in the optical domain and was earlier used for the ultraviolet metasurface design.²⁹ 

The metalens is designed as a 2D square grating of holes of different diameters milled into niobium pentoxide Nb₂O₅. Its refractive index and extinction coefficient measured by spectrophotometry combined with fitting using the Tauc–Lorentz dispersion model are shown in Fig. 1(a). The design of the hole grating is schematically shown in Fig. 1(b), where the overall size is 4 µm and the period is 250 nm. The focusing ability of the metalens is provided by a gradient of the refractive index, which turns the planar incoming wavefront into a focusing spherical wavefront. The refractive index gradient is introduced following the hyperbolic secant distribution equation (1), where n_eff is the effective refractive index of the metalens, n₀ is the initial refractive index of the selected material, and x is the varying coordinate,

Parameter α is calculated with Eq. (2), where x₀ defines the lens size (it changes from −x₀ to x₀) and n_x0 is the value of the effective refractive index at the edge of the structure (at x = x₀). Although such structures are often designed in the cylindrical coordinates,^23,25 we use the Cartesian system because we aim at applications integrating arrays of metalenses on arrays of pixelized photodetectors, which follow a square lattice,

To introduce the effective index profile, we perforate apertures of a varying diameter d(x) calculated with Eq. (3), where p is the structure period and F(x) is a filling fraction calculated using the Maxwell–Garnett mixing rule adjusted for the dielectric mixtures [Eq. (4)],³⁰ 

It states that in the case of sub-wavelength inclusions, it is possible to consider the material as a mixture of constituent parts, which in our case is Nb₂O₅ and air. Many homogenization approaches were developed for this type of problem, but this simple technique already provides a sufficiently good description. The resulting effective refractive index profile is shown in Fig. 1(c): the profile calculated analytically with Eq. (1) is shown with a solid line and the actually simulated one is shown with points connected by a dashed line. Minimum aperture size was limited to 100 nm in order to perform fabrication by FIB lithography without requiring to elaborate structures or fabrication. Therefore, in the central part of the lens, there is a mismatch between the ideal and the simulated profile. Once we have the refractive index variation, we select the metalens thickness as h = 510 nm, allowing to estimate the phase shift ϕ(r) introduced to the transmitted beam [Eq. (5)]. For the chosen operation wavelength λ = 590 nm (which is a wavelength of operation of a typical silicon photomultiplier that we see as a potential application of this work), the resulting ideal and actual phase profiles are shown together with the refractive index in Fig. 1(c),

First of all, the calculated meta-lens was simulated in the CST Studio Suite (r) on an infinite borosilicate glass substrate (n_sub = 1.52) with a plane wave (λ = 590 nm) coming at normal incidence. To demonstrate focusing, the XZ-cross section of the normalized intensity in the substrate below the meta-lens is plotted in Fig. 1(d). In addition, the XY-cross section corresponding to the best focus position [the white dashed line in Fig. 1(d)] is shown in Fig. 1(e).

The designed metalens was fabricated using a Focused Ion Beam (FIB) milling technique. The Scanning Electron Microscopy (SEM) image of the fabricated structure is shown in Fig. 1(f). Afterward, it was characterized by scanning optical microscopy with the metalens being illuminated from the air side (λ = 570 nm–610 nm) and focusing light in the substrate. For a full characterization, images were taken in several planes. First, images were taken in the XZ-plane [Fig. 2(a)] showing the long focusing spot with the 5.8 µm Full Width at Half Maximum (FWHM) along the propagation direction (which is a large depth of focus). Second, images were taken in the XY-plane [Fig. 2(b)] at the best focus position shown with a white dashed line in Fig. 2(a). The difference between the best focal positions for the simulated [Fig. 1(d)] and measured [Fig. 2(a)] lens can be explained by the overall bias in aperture sizes. Our simulations show that increasing all the aperture sizes in 20% leads to the best focal position shift from ≈8.5 µm to ≈5.7 µm away from the lens.

The images in Figs. 2(a) and 2(b) show that light transmitted through the metalens is focused within a 950 nm by 770 nm spot (4.5% of the total area) with maximum concentration factor C ≈ 5 defined as the ratio of irradiance on the surface of the concentrator to the irradiance in the detection region,³¹ which is equivalent to the ratio of intensities in this case.³² Slight astigmatism between the X- and Y-axis indicated by the 20% difference in their respective FWHM values is not an effect due to polarization (we use a non-polarized halogen lamp) but is rather connected to the slightly asymmetric shape of the holes milled in the metalens [the SEM image Fig. 1(f)]. Nevertheless, without any post-processing of the image (deconvolution from the microscope point spread function) and despite some nanofabrication imperfections, the focus spot remains below 1 µm². Finally, several XY-crosscut images were recorded at several z positions: the best focal positions are f − 4 µm, f + 4 µm, f + 6 µm to fully characterize the propagation, as shown in Fig. 2(c). Altogether, the data in Fig. 2 demonstrate the excellent optical performance of our simple and scalable metalens design. The system is also robust to the minor nanofabrication defects. Contrarily to resonant metasurfaces, our refractive index gradient approach does not require perfect control on each hole size or position. Metalens performance is also illustrated with a video (supplementary material) demonstrating white light (halogen lamp, λ from 500 nm to 650 nm) focusing: the XY-crosscut of the image was taken at different Z-coordinates varying from 0 μm to 15 µm and back. In this video, there are six samples with different milling depths ranging from ≈400 nm deep (on the left) to ≈500 nm (on the right), and the second sample from the right is the metalens shown in Fig. 2. This video confirms the excellent performance of the metalens in the bright field with the spectral range from 500 nm to 650 nm.

To assess the restrictions induced by the limited minimum size of the holes milled into niobium pentoxide, we model the metalens considering the apertures of diameters d > 20 nm [Fig. 3(a) for the XZ-crosscut and Fig. 3(f) for the XY-crosscut]. In this case, the observed focal spot is smaller in comparison to the design with d > 100 nm [Figs. 3(b) and 3(g), respectively]. However, due to the choice of the square lattice, a small part of the light is directed away from the focus, which results in the decrease in the intensity enhancement. Therefore, for a given geometry, limitation to sizes bigger than 100 nm does not hamper the optical performance and can even improve slightly the peak intensity at the focus. Then, to study the broadband behavior of the metalens with d > 100 nm, it was simulated at several wavelengths such as λ = 490 nm, 540 nm, 590 nm, 640 nm, and 690 nm. The results [Fig. 3(c)] show that, although the maximum focal spot shifts along the z-direction, the intensity enhancement stays high in the broad wavelength range, and in the case of a photodetection application, the detection region could be placed in such a way that the electron–hole generation probability would be optimal in a large wavelength region.

To estimate the sensitivity to the fabrication error, we simulate the metalens with d > 100 nm [Fig. 3(b)] with the aperture diameter taken randomly from the normal distribution with a standard deviation σ = 10 nm, where the mean value is a calculated diameter for a given spatial point (188 nm, 161 nm, 134 nm, or 109 nm). The results [Fig. 3(d)] show no major decrease in the intensity enhancement, which further demonstrates the design robustness. Then, to analyze the effect of non-verticality of the fabricated apertures, we simulate the metalens using truncated cones instead of the cylinders with perfectly vertical walls—the top base diameter equals to d and the bottom one equals to 0.6d. Figure 3(e) shows that this leads to a non-negligible decrease in intensity enhancement, which, however, matches better with the measurement results [Fig. 2(a)]. Finally, we simulate the unit cells with the different aperture diameters using periodic boundaries to compute transmittance amplitude and phase. These two quantities calculated in the case of cylindrical and conical apertures are shown in Fig. 3(h) as a function of the aperture diameter d. The difference in the phase profiles explains the focusing efficiency drop in the case of the conical apertures, which is straightforwardly explained with the homogenization model as well, as it changes mixture proportions and results in a smaller effective refractive index contrast. Moreover, the results shown in Fig. 3(h) allow calculating the average transmittance amplitude, which is T ≈ 0.93 in the case of cylindrical apertures for both profiles with d > 20 nm and d > 100 nm and in the case of conical ones with d > 100 nm.

To demonstrate the scalability of our design, we investigated the potential of a Fresnel metalens composed of eight different concentric sections (Fig. 4). The purpose of these sections is, as in a regular Fresnel lens, to enable a short focal length together with a large lens diameter without requiring very thick materials. The fabricated Fresnel metalens of dimensions 17 × 17 μm² has been characterized with the same method as the metalens in Fig. 2. The optical microscope images taken at the metalens surface and at its best focus plane are shown in Figs. 4(b) and 4(c), respectively. From the axial shift between these two planes, we deduce that this Fresnel metalens has a focal length of 7 µm. Considering the 17 µm dimension of the lens and the 1.5 refractive index of the medium where the light is focused, this Fresnel metalens features an impressive numerical aperture of 1.15. While the concentric sections intrinsic to the Fresnel design introduce interference ripples around the focal spot (as we work under the spatial coherent condition with plane wave illumination), the focal spot still bears transverse dimensions well below 1 µm demonstrating efficient focusing. Crosscuts through the focal spot along the horizontal [Fig. 4(d)] and the vertical [Fig. 4(e)] directions indicate better intensity distribution. A local intensity enhancement about 8 together with the FWHM of 800 nm shows the ability of the lens to concentrate light in a tiny spot. Comparing our results with other approaches, high-index microspheres were demonstrated to focus visible and infrared light into spots of approximately one wavelength^33,34 or even half a wavelength^35–37 in FWHM. Besides, silicon cones were used for mid-infrared and long-infrared photodetectors.³⁸ The solid immersion metalens achieved a FWHM of about 2 λ,³⁹ while monolithically integrated metalenses also focus infrared light into spots of one wavelength in FWHM.⁴⁰ Here, our results achieved in the visible spectral range are at the same level than the state-of-the-art for flat components.

We have developed a polarization-independent broadband efficient metalens and fabricated it with the CMOS-compatible technology. Our results show that the metasurface transmits light with high transmission efficiency (estimated as T ≈ 0.93), which is then focused on a 950 nm by 770 nm spot occupying ≈4.5% of the total area in the center below it with the fivefold maximum concentration factor reached. The focusing spot is spanning for 5.8 µm in the z-direction, which leaves flexibility for the detection region choice.

The produced metalens can be used for improving the photodetection efficiency (PDE) of silicon photomultipliers by reducing the amount of light that would hit the non-active area at the edge of the single-photon avalanche photodiode (SPAD), which is equivalent to reducing the influence of the fill factor (FF) on the PDE.⁴⁰ The situation is illustrated in Fig. 3(i), where the light that was supposed to enter the non-efficient zone close to the border is concentrated at the center of the detection region. Apart from reducing the influence of the FF, focusing light in a small area should allow for creating a smaller electron–hole generation region, which is beneficial for the avalanche generation and signal formation homogeneity. Our metalens design is a step toward ≈100% FF light detection, and it also gives the opportunity to increase the width of the dead border even in very small cells (≤5 µm). This approach is fully scalable and can be easily integrated with any pixelized photodetector array.

All simulations are performed using the commercially available software CST Studio Suite (r). The entire metalens was simulated with the transient solver based on the Finite Integration Technique (FIT). These simulations were done using “open” boundary conditions in the x- and y-direction, which corresponds to a single lens perforated in the infinite film in x- and y-directions. To reduce the computation time, we set the background media to be glass with n = 1.52 and artificially fill apertures and the space above the metalens with the vacuum. The excitation source is a plane wave (linearly polarized light with the electric field along the x-direction) coming from the vacuum side, and a field monitor “Power” is set to allow for the extraction of the maximum value of the Poynting vector (P) within one period of time as a function of the coordinate. Finally, we compute the spatial distribution of the transmission coefficient as a ratio between the Poynting vector calculated in the presence and in the absence of the metalens. This method is equivalent to calculating the transmission coefficient as a ratio of field intensities.³² The unit cell performance as a function of the aperture diameter was simulated using a frequency-domain solver combining the finite element method with special broadband frequency sweep techniques. We used a unit cell boundary condition that considers a periodic structure and provides a complex transmission coefficient as a result.

A 510 nm thick layer of Nb₂O₅ was deposited on glass substrates using plasma-assisted electron beam deposition (Bühler SYRUSpro 710). A high density, high uniformity layer was achieved using this technique. The precise thickness was monitored using in situ direct optical monitoring (Bühler OMS 5000) at 550 nm. A thin 10 nm additional aluminum layer was deposited on top of the Nb₂O₅ layer using the same technology but unassisted to make the structure conductive and remove electrical charges during etching. The metalens concentrator design used for the numerical simulations was converted using a MATLAB code to generate the pattern compatible with the focused ion beam system (FEI dual-beam DB235 Strata). The pattern was milled using a focused ion beam with a gallium-based source using 30 keV energy and a 10 pA beam current. Scanning electron microscopy images were performed at 5 keV energy with the Schottky Field Emission Gun (SFEG) source of the electron column.

Optical microscopy experiments are based on a home-made microscope system derived from a confocal setup reproducing the conditions used in Ref. 35. The illumination uses the in-built halogen lamp from the Nikon Eclipse inverted microscope. The field and aperture diaphragms are closed to the maximum so that the light beam emerging from the condenser lens illuminating the sample is nearly collimated. The sample containing the metalens is illuminated from the air side, and the apertures milled in niobium pentoxide are filled with air. The characterization of the light focused by the metalens is performed from the borosilicate glass substrate (with the refractive index of the substrate being 1.52). We use a Zeiss C-Apochromat 63 × 1.2NA infinity-corrected water-immersion objective to image the metasurface lens focus. A 30 µm pinhole conjugated with the microscope objective focus plane using a 164 mm Zeiss tube lens defines the confocal detection volume and provides the lateral and axial sectioning. A 3-axis piezo stage (Polytec PI P-517.3CD) scans the sample respective to the fixed detection and illumination. The intensity measurement is performed with an avalanche photodiode (MPD-5CTC, Picoquant) positioned after the pinhole connected to a photon counting module (Hydraharp 400, Picoquant). A bandpass filter (ZET405/488/565/640mv2, Chroma) selects only the light in the 570 nm–610 nm spectral window.

See the supplementary material for Zscan_whitelamp_subtitles.mp4: a video demonstrating the white light propagation 15 µm below six metalens samples with varying milling depths.

E.M. and S.E. conceived the design, E.M. performed theoretical and numerical calculations, J.L. provided technical support on the materials and coordinated the deposition of the Nb₂O₅ thin film, J.-B.C. fabricated the sample, J.W. characterized the sample, M.S. conceived and planned the Photoquant project, M.S., M.P., P.L., E.A., S.E., and A.G. supervised and coordinated the project, A.F., A.G., and G.P. provided technical support on the photodetector structure and requirements, and E.M. wrote the manuscript with support from J.W., S.E., R.A., J.L., and M.S. All authors provided critical feedback and revised the manuscript.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

This work was done in the frame of the project Photoquant, which has received funding from the ATTRACT project funded by the EC under Grant Agreement No. 777222. This project was initiated by the ERC Advanced Grant TICAL (Grant Agreement No. 338953). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 723241).