A metasurface is made up of artificial sub-wavelength structures, which can shape wavefronts of light in arbitrary ways according to the generalized Snell’s law^[1,2]. Metasurfaces have the properties of ultra-thin thickness, light weight, and high degree of design freedom, which may greatly reduce the size and complexity of traditional optical systems^[3–5]. In the last decade, remarkable progress has been made in studies of metalenses with various capabilities, e.g., small chromatic dispersion^[6], large field-of-view^[7], tunable focal length^[8], and high numerical aperture^[9]. On the other hand, the fabrication of metalenses is compatible with the complementary metal–oxide semiconductor (CMOS) fabrication process^[10–12]. Several studies about the wafer-scale fabrication of metalenses have been reported. For example, Kim et al. demonstrated the low-cost and high-throughput fabrication of large-aperture metalenses^[13]. Hu et al. reported mass-producible amorphous silicon metalenses on a 30.48 cm glass wafer^[14]. In addition, a centimeter-scale all-glass metalens using deep-ultraviolet projection stepper lithography was reported by Park et al.^[15].

Despite the advances in metalens manufacturing processes, there are inevitable process-induced defects during the actual device fabrication due to the imperfect lithography, dry etching, and thin-film deposition processes. The unit cells of a metasurface are usually designed based on the electromagnetic resonance mechanism, making them sensitive to various structural defects^[16]. Thus, the amplitude, phase, or polarization of electromagnetic waves may vary significantly when a metasurface has a substantial number of defects. Therefore, the investigation of process-induced defects is of great significance for the mass production of metalenses. Some researchers have used simulation techniques to investigate the effect of fabrication defects on the performance of metalenses, such as the inclination of sidewall tilting, lateral and longitudinal dimension variations, and random defects^[17–24]. However, it is imperative to conduct experimental investigations on the impact of defects on the optical performances of metalenses, as it significantly enhances the understanding of performance variations caused by manufacturing errors.

In this work, the impacts of process-induced defects on optical performances of near-infrared (NIR) metalenses are investigated experimentally. Four typical types of potential process-induced defects are studied, including the critical dimension (CD) bias, random missing pillars, void block defects, and solid block defects. By introducing these process-induced defects in design deliberately, NIR metalenses with different types of defects are fabricated and characterized. The focusing intensity, modulation transfer function (MTF), and Strehl ratio are analyzed to characterize the focusing performances of metalenses with defects at $\lambda =940\mathrm{nm}$.

In the design of a metalens, the transmission phase can be controlled by adjusting the diameter ($d$) of nanopillars as the effective refractive index changes. The required phase profile for a focusing metalens is given by $$\varphi (x,y)=-\frac{2\pi }{\lambda }(\sqrt{x^2+y^2+f^2}-f),$$(1)where $\lambda$ and $f$ represent the wavelength and focal length, respectively, and $x$ and $y$ represent the coordinate position on the metalens.

To obtain the transmission phase, a commercial finite difference time domain (FDTD) simulation software, Ansys Lumerical, was used in this work. The designed metalens consists of amorphous Si (a-Si) nanopillars on silicon dioxide (${\mathrm{SiO}}_2$) glass substrates. According to the ellipsometry measurement results, the refractive indices $n$ of a-Si and ${\mathrm{SiO}}_2$ are 3.0 and 1.47 at $\lambda =940\mathrm{nm}$, respectively. The a-Si nanopillars with a height ($H$) of 690 nm are periodically arranged in a square lattice with a period ($P$) of 480 nm. The simulated transmission and phase as a function of pillar diameter at $\lambda =940\mathrm{nm}$ are presented in Fig. 1(a). It shows that the phase shift can cover 0 to $2\pi$ when the pillar diameter varies from 120 to 360 nm; meanwhile, the transmission is close to 1.

In this work, the metalens’s performances with four types of process-induced defects were analyzed. Figure 1(b) illustrates the CD bias ($\mathrm{\Delta }d$) of nanopillars, which is defined as the deviation between the experimental and designed diameters. Figure 1(c) shows the random missing pillars of the metalens. The block defect, such as a void block or a solid block of the metalens, is represented by a disk area with a diameter $D$, as shown by Figs. 1(d)–1(e). The $\mathrm{\Delta }L$ presents the center-to-center distance between the disk and the metalens.

The metalenses were fabricated through the following processes. First, a 690-nm-thick a-Si thin film was grown on a 500-µm-thick fused silica substrate using plasma-enhanced chemical vapor deposition (PECVD). Following the electron beam lithography (EBL), the pattern was transferred by the lift-off process of chromium (Cr), which was used as the hard mask for dry etching of the a-Si. A reference device without the intentionally designed defects was also fabricated. The tilted-view scanning electron microscope (SEM) images of the reference device are shown in Figs. 1(f) and 1(g). All metalenses have a diameter of 180 µm.

The schematic drawing of the measurement setup is shown in Fig. 2. The 940 nm single-frequency narrow-linewidth laser is connected to a collimator through the polarization-maintaining fiber, and then the metalens sample is illuminated by a collimated laser and generates a focal point. An objective lens, a tube lens, and a Hamamatsu CMOS camera (C13440-20CU) are connected together to form an imaging system, which is used to capture focal planes of metalenses by moving the imaging system during the measurement process. The intensity distributions are measured at different focal lengths. The focal length is defined as the distance from the focal plane to the center of the metalens. According to the measurements, the focal lengths of the fabricated metalenses are within $330\mathrm{\mu m}\pm 5\mathrm{\mu m}$, corresponding to a numerical aperture (NA) of around 0.26.

The CD bias is common in nanofabrication processes, which is reflected in the diameter variation of nanopillars compared to the designed values. We consider a 25% error margin of the minimum $d$ of ideal pillars, which means $\mathrm{\Delta }d=\pm 30\mathrm{nm}$. It should be noted that all pillars are designed with the same $\mathrm{\Delta }d$ in this work. The change of $\mathrm{\Delta }d$ in the manufacturing process is realized by controlling the change of $\mathrm{\Delta }d$ in the layout. Figure 3(a) shows normalized focal plane intensity profiles of the metalenses. The optical microscopy image of the metalens with $\mathrm{\Delta }d=30\mathrm{nm}$ is shown in Fig. 3(b).

Figure 3(c) shows the top-view SEM image of a set of pillars with $d=250\mathrm{nm}$ as the reference. It is observed that the measured CD bias of these pillars is no more than 3% of the designed value, indicating a good CD control of our fabrication process. Figure 3(d) shows normalized intensity cross-sections of focal spots with different $\mathrm{\Delta }d$. The results reveal that a larger $|\mathrm{\Delta }d|$ generally leads to a lower focal spot intensity, which reaches the lowest value when $\mathrm{\Delta }d=30\mathrm{nm}$. Figure 3(e) shows the changes in focusing efficiency. The focusing efficiency is defined as the ratio of the total electric field intensity in a circular aperture with three times the full width at half-maximum (FWHM) of the focal spot to the total electric field intensity of incident light, which is commonly used in metalens design^[25]. It can be observed that the focusing efficiency decreases with increasing $|\mathrm{\Delta }d|$, with the lowest relative intensity of around 33% when $\mathrm{\Delta }d=30\mathrm{nm}$. From Fig. 3, it is also observed that the intensity and focusing efficiency decay faster when $\mathrm{\Delta }d$ is positive than that when $\mathrm{\Delta }d$ is negative in the experimental results. The probable reason for this phenomenon is that a positive $\mathrm{\Delta }d$ leads to a decrease in the gap between the pillars, which increases the depth-to-width ratio. Considering the pillar height of 690 nm and the possible minimum gap of only around 90 nm, a relatively large depth-to-width ratio raises the likelihood of non-ideal conditions occurring during the manufacturing process. These non-ideal conditions may reduce the focusing performance of the metalens. Conversely, when $\mathrm{\Delta }d$ is negative, the depth-to-width ratio becomes smaller. A relatively small depth-to-width ratio may reduce non-ideal conditions in the manufacturing process compared to a larger depth-to-width ratio.

The MTF is one of the metrics that describes the image quality. To calculate the MTF, the point spread functions (PSFs) are obtained from the measured images of the focal plane. Then the optical transfer function (OTF) can be obtained by performing a Fourier transform on the PSFs, and the MTF is calculated by taking the modulus of the OTF and normalizing it. The MTF curves of the metalenses with various CD biases are shown in Fig. 3(f). The decrease of MTF indicates a worse imaging quality of the metalenses at $\lambda =940\mathrm{nm}$. The sudden drop in all the MTF near $\sim 20\text{cycles/}\mathrm{mm}$ is attributed to the limited sampling points. Besides, limited sampling points also contribute to a relatively lower measured MTF, thus appearing to be further away from the diffraction limit. In our measurement setup, the tube lens itself exhibits some imperfections. Specifically, it is not horizontal and possesses a tilt angle of less than 1°, resulting in asymmetry in all the measured PSFs. This asymmetry is a common occurrence in non-vertical optical paths and does not affect other measurement results.

In addition, the reference metalens with a Strehl ratio larger than 0.8 exhibits diffraction-limited performances, while the Strehl ratio falls below 0.8 due to the implementation of CD bias, as shown in Fig. 3(g). The decline of the focusing intensity, MTF, and Strehl ratio reveals the deterioration of focusing performances of a metalens with CD bias, which might be explained by the following reason. As most of the pillar diameters are drifted by $\mathrm{\Delta }d$ during fabrication, the phase and transmission will shift along the horizontal axis by $\mathrm{\Delta }d$. Because the phase-diameter relationship is non-linear and the transmission is not a fixed value, the phase and transmission of the pillars are different after shifting, leading to deviations of focusing performances from design. However, it is observed that the MTF values do not change significantly with the increase of pillars $\mathrm{\Delta }d$, as the MTF curve is more related to the PSFs rather than the focusing efficiency of the metalens. The PSFs contain complete information about spatial resolution. Thus, the CD bias has less impact on the MTF.

Over-etching or particle contamination during fabrication may cause pillar fracture, which is a typical type of defect for metasurfaces. The metalenses with 10% to 40% random missing pillars ($m_{\mathrm{s}}$) were designed. In order to achieve random missing pillars, each pillar in the simulation is given a name in the order in which they are arranged, such as pillar 1, pillar 2, …, pillar $n$, where pillar 1 is close to the center and pillar $n$ is close to the edge of the metalens. Then, the pillars to be deleted can be randomly selected using the rand function in the scripting language of the FDTD simulator. Finally, the simulation software will convert the pattern described by the script into a graphic data system (GDS) layout, which will be used in the manufacturing process. Normalized focal plane intensity profiles of metalenses are shown in Fig. 4(a). The optical microscopy image of the metalens with $m_{\mathrm{s}}=40\%$ is shown in Fig. 4(b). The actual number of nanopillars is counted to be 75,704, which is less than 1% different from the designed value of 76,311, indicating that the fabrication process does not introduce a substantial amount of extra missing pillars as compared to the design.

Normalized intensity cross-sections of the focal spots are shown in Fig. 4(c), and Fig. 4(d) plots the focusing efficiency changes with respect to $m_{\mathrm{s}}$. As $m_{\mathrm{s}}$ increases, the measured focusing efficiency decreases to around 30%. In addition, the degradation of focusing performance is reflected in the MTF and Strehl ratio, as shown in Figs. 4(e)–4(f). The MTF declines with the increase of $m_{\mathrm{s}}$, and the Strehl ratio decreases from 0.8 to 0.7 almost linearly as $m_{\mathrm{s}}$ increases from 0% to 40%. The higher percentage of random missing pillars leads to more positions on the metalens that cannot meet the required phase in Eq. (1), resulting in a larger deviation of the actual phase profile of the entire metalens from the ideal value, which finally affects the focusing performance.

In addition to random missing pillars, in certain situations, a block region on the metalens may also collapse. This defect is approximated as a circular shape in our design, which appears as a void disk. The void disk defects with $D=30$ and 60 µm at different $\mathrm{\Delta }L$ correspond to block defect areas of about 3% and 11% of the whole metalens area, respectively. The normalized focal plane intensity profiles of the metalenses are shown in Fig. 5(a). The optical microscopy image of a metalens with $D=30\mathrm{\mu m}$ and $\mathrm{\Delta }L=50\mathrm{\mu m}$ is shown in Fig. 5(b). The detailed top-view SEM image of the void disk defect is shown in the inset. Figures 5(c)–5(d) show normalized intensity cross-sections of focal spots of metalenses with a void disk of $D=30$ and 60 µm, and Fig. 5(e) shows the focusing efficiency changes of these metalenses. For both the simulated and measured results, different locations of the void disk defects cause about 10% fluctuation in focusing efficiency when $D=30\mathrm{\mu m}$, and about 15% when $D=60\mathrm{\mu m}$. The MTF and Strehl ratio are shown in Figs. 5(f) and 5(g), respectively. For the metalens with $D=30\mathrm{\mu m}$, different $\mathrm{\Delta }L$ results in slight variations in the Strehl ratio, which is distributed between 0.75 and 0.8. In addition, the Strehl ratio has a larger fluctuation range between 0.65 and 0.75 when $D=60\mathrm{\mu m}$. When there is a void block defect on a metalens, it is equivalent to having only the substrate material in this area, which has lost the ability to accurately control the wavefront of incident lights. This leads to anomalous light rays. Therefore, the larger the void block defect area, the greater the impact on the focusing performance.

During the photolithography process, a block-shaped defect may be formed because the block area is not exposed. Contrary to the void block defects mentioned above, this would result in solid block defects. Similarly, metalenses with a solid disk $D=30$ or 60 µm were fabricated. Figure 6(a) shows the measured focal plane intensity profiles of these metalenses, and Fig. 6(b) shows the optical microscopy image of the metalens with a solid disk with $D=30\mathrm{\mu m}$ and $\mathrm{\Delta }L=50\mathrm{\mu m}$. The top-view SEM image of the solid disk defect of this metalens is shown in the inserted figure. Normalized intensity cross-sections of the focal spots of metalenses with a solid disk of $D=30$ and 60 µm are shown in Figs. 6(c)–6(d), respectively. As shown in Fig. 6(e), with the increase of $\mathrm{\Delta }L$, the measured focusing efficiencies of metalenses with $D=30$ and 60 µm have small increments of 0.01 and 0.02, respectively. Figures 6(f) and 6(g) show changes in the MTF and Strehl ratio of metalenses. Same as void block defects, the region with solid defects cannot regulate the incident light wavefront, leading to a deterioration in focusing performance. For both void and solid block defects, it is observed that the larger the defect region, the worse the focusing performance. In addition, it has a smaller impact compared to the one near the center when the block defect is located at the edge of the metalens. This is mainly because at the edge region, the phase gradient is too strong to be realized by a nanopillar with a finite physical size; thus, the sub-wavelength structures at the edges contribute less to the focusing performance of the metalens^[26].

From the discussions above, the four types of defects affect the phase profile of the metalens in different ways and finally worsen the focusing performance. For different degrees of CD bias, random missing pillars, and block defects, the focusing intensity of the metalens was reduced significantly. Besides, from the measured results of the MTF and Strehl ratio, the focal point quality becomes worse too. To achieve near-optimal performance of the metalens, process-induced defects need to be minimized. Higher resolution of lithography and optical proximity correction (OPC) technology could be used to improve the fidelity of patterns and suppress the CD bias. During the dry etching process, attention should be paid to avoid the collapse of sub-wavelength structures caused by over-etching. Particle contamination is also a major source of defects. For example, the mask contamination can affect the quality of transferred patterns. In addition, due to the small size of sub-wavelength structures of metasurfaces, removing smaller particles during the wafer cleaning is required.

In summary, the impacts of process-induced defects on the optical performances of NIR metalenses are investigated experimentally. Metalenses with different types of defects are characterized, including the CD bias, random missing pillars, void block defects, and solid block defects. Increasing the CD bias and the number of random missing pillars worsens the focusing performance of the metalens significantly. For block defects, both the position and area of the defects affect the focusing characteristics of the device. It is observed that the block defect located at the edge of the metalens has a smaller impact compared to the one near the center. This work paves the way for the mass production and commercialization of metasurface-based flat optics.