HgCdTe mid-Infrared photo response enhanced by monolithically integrated meta-lenses

Polarization-independent dielectric meta-lens is proposed to monolithically integrate with a HgCdTe infrared photodetector to concentrate power flux into a reduced photosensitive area for performance enhancement. Although a reduction in photosensitive area could suppress the dark current, the more seriously reduced light absorptance would degrade the specific detectivity D*. The integration of the meta-lens could reverse the situation by improving the absorptance of the photosensitive region. The meta-lens composed of an array of nano-pillars with varying diameters is formed by carving the CdZnTe substrate of the HgCdTe detector so that the integration could be accomplished in situ. The meta-lens focuses the incident light through the CdZnTe medium and at the HgCdTe photosensitive region. The focal spot is about the wavelength size and the focusing efficiency is above 63%. Concerning a HgCdTe detector with a pitch size of 40 μm × 40 μm, when the photosensitive area is reduced to 5 μm × 5 μm, the meta-lens could still keep the light absorptance above 50%, which is 49 times higher than that of the device without the meta-lens. The dark current reduces with the decreasing photosensitive area in a linear manner. When the photosensitive area shrinks from 40 μm × 40 μm to 10 μm × 10 μm or 5 μm × 5 μm, the dark current reduces by 16 or even 64 times. Compared to the pristine device, the employment of the meta-lens together with the reduction in photosensitive area could enhance D* by 5.5 times for the photosensitive area as 5 μm × 5 μm. Further, the meta-lens exhibits a good dispersion tolerance over the wavelength range from 3.3 μm to 5 μm. The averaged detectivity enhancement over this spectrum range is around 3 times for the photosensitive area as 5 μm × 5 μm. The angular response of the meta-lens integrated detector depends on the focal length. For a focal length of 73 µm or 38 µm, the angle of view for a 5 μm × 5 μm photosensitive area is 4.0° or 7.7°. For the inter-pillar distance to be 2 µm in our design, the influence of the coupling effect between the nano-pillars on the performance of the meta-lens is little.

developing meta-surface based flat optics provide us a new approach to concentrate light into a reduced active volume. Meta-surface has been successfully applied to control the phase, amplitude and polarization of the incident light by altering the shape and the size of each meta-unit and arranging them a proper way. In a wide range of spectrum from the visible to the terahertz band [13][14][15][16][17][18][19][20][21][22][23][24] , many optical applications based on meta-surfaces have been realized and reported, including meta-surface lenses (meta-lenses), waveplates, holograms and polarimeters [25][26][27][28][29][30][31][32] . The ultra-compact sizes of the flat optics make them promising to substitute conventional ones in some situations. Among all the flat optics, meta-lenses received the most research interest due to the broad application areas and the distinct advantages, such as self-alignment during fabrication, high numerical apertures 33,34 , and solid-immersion type of integration 35 . Meta-lenses have been demonstrated to be effective to focus the incident light through a high-index semiconductor 35 , indicating that the monolithic integration of a meta-lens into a semiconductor based infrared photodetector for light concentration in a reduced active volume is promising and feasible.
In this work, we propose to monolithically integrate a dielectric transmissive and polarization-independent meta-lens into a mesa-type HgCdTe infrared photodetector to enhance light collection in a reduced active volume for detectivity enhancement. The meta-lens is based on the all-CdZnTe meta-surface, which could be directly fabricated on the backside of the HgCdTe infrared detector by standard photolithography and etching process. For mid-infrared light with a wavelength around 4 μm, the meta-lens with a pitch size of 40 μm can focus the incident light into a small spot of the wavelength size on the photosensitive area with a full-width at half-maximum (FWHM) of 4 μm. With the help of the meta-lens, the absorptance of the photosensitive region remains above 50%, even though the photosensitive area is reduced by 64 times to 5 μm × 5 μm. The specific detectivity is enhanced by 5.5 times compared to the reference device with no reduction in photosensitive area and with no meta-lens. Further, the composite device exhibits a good dispersion tolerance over the wavelength range from 3.3 μm to 5 μm, and the averaged detectivity enhancement is around 3 times. The angular response of the meta-lens integrated infrared detector is analyzed. And the coupling effect between the nano-pillars is discussed. We envision that the monolithically integrated meta-lens is promising to improve the sensitivity of the traditional semiconductor infrared photodetectors.

Device structure
The integration of such a meta-lens with a mesa-type HgCdTe detector is schematically illustrated in Fig. 1. The HgCdTe detector is actually a single pixel of a focal plane array and ready for flip-chip bonding. The meta-lens consisting of a nano-pillar array is proposed to be fabricated by hard-mask-assisted reactive ion etching [36][37][38][39][40][41] . The hard mask made of SiO 2 can enhance the etching selectivity by over 37 times 38 compared to a photoresist mask, and then enable the formation of high-aspect-ratio structures [39][40][41] . In this case, each nano-pillar contains a SiO 2 cap on the top. By choosing a proper thickness of this mask layer, the transmission through the meta-lens is enhanced. The focal length f is determined by the thickness of the CdZnTe film, which typically varies from 30 μm to 800 μm 42 , and it is assumed to be 73 μm in this study without loss of generality. The HgCdTe layer is epitaxially grown on the other side of the CdZnTe. The active area is defined by the mesa. As the mesa size decreases, a lower dark current is expected. In order to remain the light collection efficiency, the incident light is desired to be focused into the reduced active region. As a photovoltaic HgCdTe infrared photodetector, the mesa contains P, N and N + regions. The thicknesses and doping levels of each region are set to be 9.96 μm, 0.43 μm, 2.5 μm and 8.4 × 10 15 cm −3 , 2 × 10 16 cm −3 , 2.4 × 10 17 cm −3 , respectively, as typical values for HgCdTe photodetectors operating in the mid-infrared range 43 . The mesa height is around 10 μm. For the numerical simulations, the wavelength dependent refractive index of CdZnTe follows ref. 44 . and that of SiO 2 follows refs. 45,46 . The composition of the Hg 1-x Cd x Te is set to be x = 0.276 for mid-infrared detection 47 , and the corresponding complex refractive index are obtained through refs. 48,49 .
Concerning a plane wave normally incident on the detector, the meta-lens on the top would focus the light at the interface between the CdZnTe and the HgCdTe. As illustrated in Fig. 2[a], the meta-lens is composed of an array of CdZnTe nano-pillars. The nano-pillars are formed by carving the CdZnTe substrate, which also supports the epitaxially grown HgCdTe on the other side. The circular cross section is set for polarization-independent response. Each unit cell of the meta-lens occupies a 2 μm × 2 μm square area and contains one nano-pillar at the center. All the nano-pillars are of the same height (H p = 4.23 μm and H mask = 0.73 μm), but vary in diameter according to the positions. Each nano-pillar works like a waveguide for the incident light. The dispersion relation of the waveguide mode is dependent on the diameter. As shown in Fig. 2[b], the phase of the waveguide mode advances faster in a thicker nano-pillar. Therefore, by finely controlling the diameters and the inter-distance of the nano-pillars, the outgoing phase at each unit cell could be tuned over the range from 0 to 2π while the transmittance could remain similar (Fig. 2[c]), so that the wave front of the light passing through the meta-surface could be freely designed. Ideally, the phase distribution at the plane just after a convergent lens should follow an inward propagating spherical wave, as described by where λ d denotes the operating wavelength, f the focal length and n s the refractive index of the medium. When the phase distribution of the light just passing through the nano-pillar array follows Eq. 1, the light field would converge into a spot, and the nano-pillar array just functions like a lens. For the incident wavelength of 4 μm, with the diameter d of the nano-pillar varying from 0.69 μm to 1.52 μm, a phase shift over 2π could be achieved, and the transmittance averagely reaches 90% (Fig. 2[c]). Figure 2[d] presents the required phase distribution ϕ(x, 0) along the x-axis cutting through the center of the meta-lens for the incident light to be focused at a plane 73 μm www.nature.com/scientificreports www.nature.com/scientificreports/ away from the meta-surface inside the CdZnTe substrate. As illustrated in the insert of Fig. 2[d], the meta-lens contains 21 × 21 unit cells. The nano-pillar diameters are optimized according the evaluation function () , which concerns both phase and transmittance 50 . For a nano-pillar at the position (x, y), an appropriate diameter D, which minimizes C, is selected. ϕ(D) and T(D) are the phase shift and the transmittance at the meta-element (x,y) with a nano-pillar of diameter D. T m is the averaged transmittance over all the meta-elements. The finite difference time domain method is employed to simulate the optical behavior of this device, and the simulation regime consists of three regions: the air, the CdZnTe substrate, and the HgCdTe active region. The electrical properties of the infrared detector are investigated through the technology for computer-aided design (TCAD). Figure 3[a,b] present how the incident light is focused into the CdZnTe substrate by the meta-lens. Figure 3[a] presents the distribution of the relative power flux (|P|/|P 0 |) on the x-z cross section cutting through the center of the CdZnTe supported meta-lens. It is exhibited that the incident light is focused at a plane about 73 μm below the meta-lens inside the CdZnTe. The focal spot has a full width half maximum (FWHM) of 4 μm, as revealed by the relative power flux (|P|/|P 0 |) profile ( Fig. 3[b]) along the dashed line in Fig. 3[a]. The concentrated light power at the center of the focal spot is 235 times higher than the incident power. The focusing efficiency, defined as the ratio of light power entering a square of 4 × FWHM centered at the focal spot on the x-y plane (dashed frame in the inset of Fig. 3[b]) to the total power incident on the meta-lens 50 , is above 63%. Figure 3[c] illustrates a full structure simulation of the meta-lens integrated HgCdTe detector. The incident light is successfully converged at the photosensitive region and it is quickly absorbed after penetrating into the HgCdTe. As shown in Fig. 3[d], with the help of the meta-lens, the absorptance of the photosensitive region (A meta ) remains higher than 50% for the photosensitive area larger than 5 μm × 5 μm, while in the absence of the meta-lens the absorptance of the photosensitive region (A non-meta ) degrades with the decreasing area almost linearly, indicating that the meta-lens www.nature.com/scientificreports www.nature.com/scientificreports/ could drastically enhance the absorptance for reduced photosensitive areas. Specifically, the meta-lens improves the absorptance by 49 times or 13 time for S m = 5 μm × 5 μm or S m = 10 μm × 10 μm.

Result and analysis
An infrared photodetector is evaluated not only by the photoresponse but also by the noise. For such a HgCdTe photovoltaic detector, the photoresponse is proportional to the light absorptance of the active region, and the noise is largely decided by the dark current 51 . Figure 4[a] presents the dark current (I d ) as a function of the photosensitive area (S m ) at typical operating bias voltages from −0.1 V to −0.5 V. The dark current reduces with the decreasing photosensitive area in a linear manner. When the photosensitive area shrinks from 40 μm × 40 μm to 10 μm × 10 μm or 5 μm × 5 μm, the dark current reduces by 16 or even 64 times. The reduction in dark current would steadily suppress the noise (I n ) as favored by infrared detectors. However, in the absence of the meta-lens, the light absorptance of the photosensitive region and hence the responsivity R i also decrease with S m linearly. In this case, the detectivity = ⋅Δ . S stands for the pitch area of the HgCdTe detector, which remains 40 μm × 40 μm in our case. Δf denotes the bandwidth. e is the electron charge. With the help of the meta-lens, the absorptance of the photosensitive region and hence the responsivity is significantly improved (Fig. 3[d]). As a result, D * is prominently enhanced with the decreasing S m , as shown in Fig. 4[b]. D * 0 denotes the detectivity of the HgCdTe detector with no reduction in the photosensitive area and with no meta-lens. The detectivity enhancement as represented by D * meta /D * 0 is 3.2 for S m = 10 μm × 10 μm and it reaches 5.5 for S m = 5 μm × 5 μm, indicating that the integration of the meta-lens in an infrared detector to focus light onto a reduced photosensitive area could promisingly enhance the device performance.
Although the meta-lens is not intentionally designed to be achromatic, it could still effectively enhance the detectivity of the HgCdTe detector over the wavelength range from 3.3 μm to 5 μm, as benefited from the elongation of the focal spot in the z-direction. The meta-lens is designed for the wavelength of 4 μm. At this specific wavelength, the incident light could be perfectly focused onto the photosensitive region and directly at the interface between the CdZnTe and the HgCdTe, as shown in Fig. 5[a-f]. When the wavelength deviates from 4 μm, the focal plane moves downwards or upwards due to the dispersion of the meta-lens 53 . Consequently, the field concentration at the interface between the photosensitive region and the CdZnTe substrate becomes less tight so that a part of power leaks out, leading to reduction in absorptance and responsivity.
As shown in Fig. 6[a], the absorptance of the photosensitive region reaches a maximum at the designed wavelength (4 μm) and reduces when the wavelength either decreases or increases. Fortunately, since the focal spot is elongated in the z-direction as shown in Fig. 5, the offset between the focal plane and the surface of the photosensitive region does not severely degrades the absorptance. For S m = 5 μm × 5 μm, A meta remains higher than 15.2% over the range from 3.3 μm to 5 μm and the averaged A meta reaches 27%. For S m = 10 μm × 10 μm, A meta remains higher than 22% over the same wavelength range and the averaged A meta reaches 37%. Therefore, the averaged enhancement of the absorptance over the wavelength range from 3.3 μm to 5 μm is around 24.5 times for S m = 5 μm × 5 μm and it is around 8.5 times for S m = 10 μm × 10 μm (Fig. 6[b]). Concerning the detectivity, the averaged enhancement (D * meta /D * 0 ) is around 3 times for S m = 5 μm × 5 μm and 2 times for S m = 10 μm × 10 μm (Fig. 6[c]). The good chromatic dispersion tolerance indicates that the integration of the meta-lenses and the infrared photodetectors for performance enhancement is prospective.
Moreover, the angular response of the meta-lens integrated infrared detector is important since sensing angular light is somehow demanding in real applications. Concerning the meta-lens with a focal length of 73 μm, the absorptance of the active region (5 μm × 5 μm) drops by more than a half when the incident angle increases to 5° (Fig. 7[a] black line). This degradation also occurs for traditional microlens 2,54 . Shortening the focal length is a method to alleviate this degradation. As shown in Fig. 7[a] red line, when the meta-lens is designed to have a short focal length of 38 μm, the absorptance of the active region drops much more slowly than that for the long focal length of 73 μm. At the 5° oblique incidence, the active region absorptance for the short-focal-length www.nature.com/scientificreports www.nature.com/scientificreports/ case remains 94% of that at normal incidence. This effect is also illustrated by the distribution of the power flux ( Fig. 7[b-f]). The focal spot in the short-focal-length case offsets more slowly with the incident angle than that in the long-focal-length case. Concerning focal length adjustment, especially realization of short focal lengths, meta-lenses have an advantage over traditional micro-lenses. Shortening the focal length of a meta-lens is simply to rearrange the distribution of the nano-pillars, while shortening the focal length of a traditional micro-lenses needs to enlarge the surface curvature, which takes more efforts in fabrication. Another method to alleviate the degradation with incident angle is to enlarge the active region. As shown in Fig. 7[a], when the active region is enlarged to 10 μm × 10 μm, the absorptance of the active region remains higher than 98% of that at normal incidence over for oblique incidence up to 10°. The angle of view (AOV) is defined as 2arctan(s/(2 f)) 2 , where s is the size of the active area, and f is the focal length. Another important issue for the meta-lens is the coupling between the nano-pillars. A metalens is a nonperiodic structure. However, the design of the nano-pillars is based on unit cell simulation employing periodic boundary conditions. The coupling between the nano-pillars affects the propagation constant of the waveguide mode and hence the phase accumulation. Since a nano-pillar in the meta-lens feels a different environment than in the unit cell simulation, the phase distribution over the meta-lens deviates from the design. In this work, the unit cell simulation with periodic boundary conditions is only used as the reference for preliminary design. The full-meta-lens as a nonperiodic structure is finally simulated to evaluate the performance of real device. It is true that there is deviation between the unit cell simulation and the full-meta-lens simulation. But, the deviation is small. As confirmed by Fig. 8[a], the phase distribution profile based on full meta-lens simulation (red line) deviates from the design based on unit cell simulation (black line). For the center-to-center inter-pillar distance (d inter ) as 2 μm, the focal length is about 73 μm, shorter than the designed value of 80 μm (Fig. 8[b]). The deviation is only 8.8%. The coupling between the nano-pillars is also revealed by the field distribution. As shown in Fig. 8[c,d], the light field in the space between the nano-pillars is obvious.
Although traditional micro-lens arrays have been applied to enhance the light coupling efficiency for photodetector since a long time ago 55 , meta-lenses have several potential advantages over traditional micro-lenses. Meta-lenses could achieve higher aspect ratio 33,34 than traditional micro-lenses 10,11 , and a higher aspect ratio corresponds to a big angle tolerance. Meta-lenses do not need complicated packaging and alignment since they are self-aligned once fabricated. Moreover, they are more compatible to flip-chip-bonded infrared focal plane arrays since they can be fabricated directly on the substrate for a solid-immersion type of focusing 35 . And meta-lenses can be achromatic by properly designing the multiple resonances of the unit-cells 56 , so that they are more suitable for broadband applications potentially. A more detailed comparison can be found in the Supplementary Material.

conclusion
In conclusion, a transmissive polarization-independent dielectric meta-lens is proposed to monolithically integrate with a HgCdTe infrared photodetector to concentrate power flux into a reduced photosensitive area for performance enhancement. The whole device unit can be regarded as a pixel element of focal plane, so it can be used for the integrated preparation of FPA. The meta-lens composed of an array of nano-pillars with varying www.nature.com/scientificreports www.nature.com/scientificreports/ sizes is formed by carving the CdZnTe substrate of the HgCdTe detector and an SiO 2 layer is added for higher transmission. A meta-lens integrated HgCdTe infrared photodetector with a pitch size of 40 μm × 40 μm was numerically investigated. Although a reduction in photosensitive area could suppress the dark current, the more seriously reduced light absorptance would degrade the specific detectivity D*. With the help of the meta-lens, which focuses the light into a spot of wavelength size with an efficiency over 63%, the light absorptance of a 5 μm × 5 μm or 10 μm × 10 μm photosensitive region still remains 50% or 58% although the photosensitive area is reduced by 64 or 16 times compared to the pristine. Consequently, the integration of the meta-lens enhances the D* by 49 or 14 times for S m = 5 μm × 5 μm or S m = 10 μm × 10 μm. Compared to the pristine device, the integration of the meta-lens together with the reduction in photosensitive area enhances the D * by 5.5 or 3.2 times  www.nature.com/scientificreports www.nature.com/scientificreports/ for S m = 5 μm × 5 μm or S m = 10 μm × 10 μm. Further, the meta-lens exhibits a good dispersion tolerance over the wavelength range from 3.3 μm to 5 μm. The averaged detectivity enhancement over this spectrum range is around 3 times for S m = 5 μm × 5 μm and 2 times for S m = 10 μm × 10 μm. The angular response of the meta-lens integrated detector depends on the focal length. For a focal length of 73 μm, the AOV for a 5 μm × 5 μm photosensitive area is 4.0°. When the focal length is reduced to 38 μm, the AOV for a 5 μm × 5 μm photosensitive area increases to 7.7° and it reaches 15.4° for a 10 μm × 10 μm photosensitive area. For the inter-pillar distance to be 2 μm in our design, the influence of the coupling effect between the nano-pillars on the performance of the meta-lens is little. Therefore, the monolithic integration of a meta-lens provides us a promising way to enhance the performance of infrared photodetectors and even focal plane arrays.

Methods
The performance of the proposed metalens are characterized by using the three-dimensional finite difference time domain (FDTD) method from Lumerical Inc 57 . For the simulation of the unit cell, periodic boundary conditions are applied along the x and y axis and perfectly matched layers (PML) is applied along the z axis.