Design of Broadband Infrared Photodetectors Enhanced by Dual-Mode Plasmonic Resonant Cavities

The signal-to-noise ratio of infrared photodetectors can be improved by using resonant cavities, whereas the enhancement effect usually occurs in a narrow wavelength range. Here, we propose a dual-mode plasmonic resonant cavity which can enhance the performance of infrared photodetectors in a wide range of wavelengths from 3.5 μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}m to 5.5 μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}m. The optical cavity consists of an Au grating, an ultrathin (310 nm) detective layer of mercury cadmium telluride, and an Au film, which can exhibit nearly perfect absorption at resonant wavelengths with using optimal parameters. For wavelengths from 3.5 μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}m to 5.5 μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}m, the wavelength-averaged absorption in the detective layer can also be 62%, about 12 times of that without the resonant cavity. Such a high enhancement of absorption can occur for incident light in a broad range of angle (θ<450\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta <45^{0}$$\end{document}) and with different polarizations.

Recently, metasurfaces have been constructed to realize high light absorption in a broad band, where multiple distinct metallic resonators exist in a unit cell [22][23][24]. Such metasurfaces enable strong thermal emission, whereas they cannot be directly applied to enhance infrared photodetection. To enhance infrared photodetection, detective materials need to be incorporated in the structures, and infrared light in target wavelength ranges should be absorbed mainly by detective materials rather than metal. In addition, it would be better to adopt connected metallic patterns in the metasurfaces which can serve as electronic contacts. However, such requirements have not been met in previous designs.
In this paper, we propose a plasmonic resonant cavity which can enhance the performance of infrared photodetectors in an atmospheric window with wavelengths from 3.5 m to 5.5 m. The optical cavity consists of an Au grating, an ultrathin (310 nm) detective layer of mercury cadmium telluride (MCT) [4], and an Au film. We show that by using appropriate structural parameters, two optical resonant modes can exist simultaneously in the target wavelength range (from 3.5 m to 5.5 m), and the whole structure can exhibit nearly perfect absorption at resonant wavelengths. The wavelength-averaged absorption in the detective layer over the target wavelength range can be 62%, about 12 times of that without using the resonant cavity.

Results
The photonic structure under study is an MCT layer with thickness t, which is in the x-y plane and sandwiched between an Au grating and an Au film, as shown in Fig. 1a, b. The top Au grating is an Au film perforated by a square lattice of square holes with size Δ and period a. Both the top Au grating and bottom Au film possess the same thickness t 0 , which can serve as electric contacts. The structure is illuminated by light propagating in the x-z plane that has an incident angle and wavelength . A finite element method is adopted to simulate the light absorption in the structure based on COMSOL MULTIPHYSICS commercial software. Here, the permittivity of gold Au is described by the Lorentz-Drude model [25], and the permittivity of MCT (Hg 0.83 Cd 0.17 Te) MCT is about 13 + i0.87 for wavelengths from 3.5 m to 5.5 m [26]. We first consider a photonic structure with parameters of a = 2.4 m, Δ = 0.85a , t = 0.31 m, t 0 = 0.1 m. Figure 2a shows the absorption spectrum at normal incidence, where two absorption peaks can be observed. The whole structure exhibits nearly perfect absorption at resonant wavelengths of 1 = 4.29 m and 2 = 5.11 m. The absorption in the MCT layer is about 80% at the resonant wavelengths, which is about 16 times of that in a freestanding MCT layer [ Fig. 2b]. For the target wavelength range, the MCT layer can also possess a high wavelength-averaged absorption (62%), much higher than that in a freestanding MCT layer (5%). Such a high absorption enhancement remains for a wide range of incident angles ( < 45 0 ) and for different polarizations [ Fig. 2c, d].
The distribution of electromagnetic power loss density q in the MCT layer is also calculated at resonant wavelengths, as shown in  Fig. 3b], maximal absorption exists at lower resonant wavelengths [7] (1) R1 = 2nt∕m, Such a resonant mode can split into two modes when an Au grating is covered on the MCT-Au bilayer structure, as shown in Fig. 3c. For the fundamental mode with m = 1 , the mode splitting occurs in a wide range of thickness (0.2 m < t < 0.5 m). As will be shown, the occurrence of the mode splitting strongly depends on the parameters of the Au grating including the hole size Δ and period a. If the hole size or the period is much smaller than the working wavelength ( Δ < 0.3 R2 or a < 0.3 R2 ), the Au grating will behaves like a uniform film so that the fundamental resonant mode will not split. This also explains why the mode splitting effect has not been discovered in previous studies [7]. In fact, when the period is much smaller than the working wavelength, the top Au grating will provide the same reflection phase as the bottom Au film, and thus the resonant wavelength of the Au grating-MCT-Au sandwiched structure will be given by Eq. (1) [7]. Figure 3d shows the wavelength-averaged absorption in the MCT layer over the target wavelength range for the three structures. Since two absorption peaks simultaneously occur in the target wavelength range, the Au grating-MCT-Au sandwiched structure enables higher wavelength-averaged absorption in the MCT layer than the other two structures. When the thickness t = t opt = 0.31 m, the MCT layer in the sandwiched structure can possess a maximal average absorption in the target wavelength range. Such an optimal thickness can also be estimated by where c = 4.5 m is the central wavelength of the target spectral range.
The two absorption peaks in Fig. 2 originates from the splitting of the fundamental resonant mode with m = 1 in the MCT-Au bilayer structure. To learn more about the mode splitting effect, we simulate the sandwiched structures with different hole size Δ in the Au grating, as shown in Fig. 4a. Here, the parameters are a = 2.4 m, t = 0.31 m, and t 0 = 0.1 m. When Δ = a , a single resonant mode occurs at wavelength of R2 = 4.5 m. When the hole size of grating Δ is appropriately chosen ( 0.76 < Δ∕a < 0.9 ), the resonant mode will split into two modes at wavelengths of 1 and 2 where R2 = 4nt , and 1 = −1.44 m and 2 = 9.33 m for a = 2.4 m. The difference between the two resonant wavelengths increase with decreasing the hole size. Compared with the larger resonant wavelength 2 , the smaller resonant wavelength 1 is closer to the original resonant wavelength R2 . The wavelength-averaged absorption ⟨A⟩ in the MCT m. c Absorption spectrum and d wavelength-averaged absorption ⟨A⟩ in the MCT layer as a function of period a with Δ = 0.85a . ⟨A⟩ is the averaged absorption for wavelengths from 3.5 m to 5.5 m layer over the target wavelength range strongly depends on the hole size. When Δ∕a = 0.85 , the average absorption ⟨A⟩ in the MCT layer can reach maximum (62%), as shown in Fig. 4b. When Δ∕a < 0.3 , the sandwiched structure will not enhance the absorption in the MCT layer.
We also investigate the influence of the grating period a on the absorption in the MCT layer in the sandwiched structure, as shown in Fig. 4c. Here, the parameters are Δ∕a = 0.85 , t = 0.31 m, and t 0 = 0.1 m. When a < 0.35 c , a single resonant mode exist in the target wavelength range and the wavelength-averaged absorption in the MCT layer increases with increasing the period a, as shown in Fig. 4d. However, when a > 0.35 c , two resonant modes occur in the target wavelength range, resulting in a high wavelength-averaged absorption in the MCT layer (from 54% to 64%). Here, the smallest optimal period can be estimated by When the optimal period is adopted, the wavelengthaveraged absorption in the MCT layer over the target wavelength range can reach a local maximum (62%).

Conclusion
In summary, we have investigated the enhancement effect of a plasmonic resonant cavity on MCT infrared photodetectors working in the wavelength range from 3.5 m to 5.5 m. The resonant cavity is composed of an Au grating, an MCT layer, and an Au film, which can support two resonant modes in the target wavelength range. By optimizing the structural parameters, the whole structure can exhibit perfect absorption at resonant wavelengths. The wavelength-averaged absorption in the MCT layer over the target wavelength range can be 62%, about 12 times of that without the resonant cavity. Such a high enhancement of absorption can occur for incident light in a broad range of angle ( < 45 0 ) and with different polarizations.

Data Availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations
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Conflicts of Interest
The authors declare no competing interests.