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Metamaterials-based broadband absorption in long-wave infrared frequency enabled by multilayered ENZ films on metal-coated patterned silicon

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Abstract

Large-scale, and high-throughput produced devices with strong ultrabroadband absorption and high angular tolerance are in demand for applications such as thermal imaging, energy harvesting, and radiative cooling. Despite long-standing efforts in design and fabrication, it has been challenging to achieve all these desired properties simultaneously. Here, we create a metamaterial-based infrared absorber fabricated from thin films of epsilon-near-zero (ENZ) materials grown on metal-coated patterned silicon substrates that exhibit ultrabroadband infrared absorption in both p- and s-polarization at angles ranging from 0° to 40°. The results show that the structured multilayered ENZ films exhibit high absorption (> 0.9) covering the entire 8∼14 µm wavelengths. In addition, the structured surface can be realized via scalable, low-cost methods on large-area substrates. Overcoming the limitations on angular and polarized response improves performance for applications such as thermal camouflage, radiative cooling for solar cell, thermal image and et., al.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Since the first demonstration of metamaterial-based perfect absorbers (MPAs) [1], the advent of metamaterials has spawned extensive research into MPAs over the last decade. Due to their diverse properties, MPAs have been demonstrated in many applications, such as photodetection [2], solar cell [3], thermophotovoltaics [4], sensing [5,6], structured color [7], etc.

However, the bandwidth of the MPA’s absorption is limited by localized plasmonic resonances. Nevertheless, a wider bandwidth with high absorption is more favorable in most of practical applications, such as thermal imaging [8], solar energy harvesting [9], infrared stealth [10,11], radiative cooling [12,13], etc. Several different methods have been proposed to implement broadband absorption. One approach is achieved by superimposing of multiple resonant modes via tailoring the size of top patterned metallic layer (planar arrangement) or vertically stacking multiple patterned metallic layers (vertical arrangement) to form broadband absorption [14,15]. Moreover, the high loss in metallic components of the metamaterial absorbers can also significantly broaden the absorption bandwidth [16]. Recently, some works demonstrated that a nanofilm of ENZ material can significantly broaden the absorption band with incorporation of the ENZ nanolayer between the top patterned metallic layer and the dielectric spacer layer of a metal-insulator-metal (MIM) plasmonic structure [17,18]. Another approach has been proposed to achieve perfect broadband absorption by the collective excitation of the slow-light waveguide modes in tapered metal/dielectric stack-based hyperbolic metamaterials (HMMs), such as sawtooth, [19], nano-cone [20], and pyramids [21].

Yet, in those above-mentioned works, some sophisticated nanofabrication, such as Electron Beam Lithography (EBL) and Focused Ion Beam (FIB), was required to fabricate the metallic nanostructures to stimulate the localized surface plasmon polariton (LSPP) resonances within the infrared frequency, which is considered as a serious barrier on the way to the large-scale and high-throughput production.

To overcome these barriers, researchers have come up with some easy-to-fabricate structures that consists of multilayered materials. Recently, a graphene-based hyperbolic metamaterial has been proposed to realize the critical coupling effect, and a near-perfect absorption can be obtained by changing the Fermi energy level of the graphene sheets [22]. Atomically thin two-dimensional (2D) materials provide a powerful platform for manipulation of the light [23], however the preparation of 2D materials and fabrication of nanostructured 2D materials remain challenges. Recently, a narrowband multi-frequency directional infrared absorption has been demonstrated in ultrathin, Berreman-mode-supporting cadmium oxide (CdO) multilayer stacks [24]. And broadband directional absorption has been demonstrated by introducing gradient epsilon-near-zero materials directly deposited on a metal substrate [25,26]. The ultrathin ENZ film on a metal can support a leaky TM mode near the frequency of the longitudinal optical (LO) phonon polariton, named Berreman mode [27,28]. However, in flat films configuration, the Berreman modes only couple to p-polarized light and exhibit highly off-normal absorption angle. A recent work reported by Livingood et al. [29] demonstrated that a thermal emitter fabricated from thin films of doped CdO grown on patterned sapphire substrate can exhibit polarization-independent narrowband infrared absorption around the surface normal. Despite the proposed devices have solved the limitation of polarized and angular response, the broadband omnidirectional absorption is still proven to be a difficult task.

In this paper, we present a cost-effective structure consisted of multilayer stack of gradient ENZ materials grown on metal-coated patterned silicon substrates to achieve broadband near-perfect absorption in the long-wavelength infrared (LWIR) range. This is realized through the superposition of narrowband and polarization-independent absorption of both ENZ modes and transverse optical (TO) phonon resonances excited within the multilayered polar dielectric materials. By growing the gradient ENZ materials upon a metal-coated patterned silicon substrate, the absorption is no longer restricted to incident angles and polarizations, and instead resulting in an ultrabroadband near-perfect absorption in both s- and p-polarizations. The structured surface can be realized via scalable and low-cost methods on large-area silicon substrates. This non-lithographic technique is compatible with standard microfabrication methods, enabling large-scale production of ultrabroadband infrared absorbers for applications in microbolometers, radiative cooling et al.

2. Materials and methods

The ultrabroadband near-perfect absorption of proposed device is based on the excitation of the ENZ modes and transverse optical (TO) phonon resonant mode within the ENZ films. The ultrathin ENZ film on a metal substrate can support both Berreman and ENZ modes [27,28] that are spectrally located near the zero-crossing of the real permittivity (ωENZ), with the former located above the free-space light line, thus being accessible from free-space and providing near-unity absorption of p-polarized light at a certain incident angle (near the Brewster condition). The dispersion of ENZ mode is right below the free-space light line, and thus require an additional momentum to be excited.

The Berreman mode occurs only in p-polarized oblique incidence, the reflectance exhibits a pronounced minimum for an ENZ film thickness (known as Berreman thickness) [30]

$${h_\textrm{B}} = \frac{{{\lambda _\textrm{B}}}}{{2\pi }}\frac{{\cos \alpha }}{{{{\sin }^2}\alpha }}{\left[ {{{\left. {{\mathop{\rm Im}\nolimits} \left( { - \frac{1}{\varepsilon }} \right)} \right|}_{\max }}} \right]^{ - 1}}$$
where λB is the Berreman wavelength, α is the incident angle, ε is the permittivity of ENZ film.

According to the Eq. (1), the Berreman wavelength is decided by the peak of the energy-loss function Im (−1/ε), as shown in Fig. 1(a3-f3). Here we consider six polar dielectric materials: SiO2, Si3N4, Al2O3, AlN, TiO2, and α-Ta2O5, whose Berreman wavelengths obtained from the peaks of energy-loss function are 8.15 µm, 9.67 µm, 10.69 µm, 10.93 µm, 11.71 µm, and 11.07/12.37 µm, respectively. The dielectric permittivities of SiO2. Si3N4, Al2O3, AlN, TiO2 are taken from Kischkat et al [31], and the dielectric permittivity of α-Ta2O5 is taken from Bright et al [32].

 figure: Fig. 1.

Fig. 1. Simulated p-polarized reflective spectra varying with incident angle and wavelength for ENZ films with different thickness on aluminum (Al) substrate, (a1) 0.1 µm and (a2) 0.74 µm SiO2, (b1) 0.2 µm and (b2) 0.5 µm Si3N4, (c1) 0.2 µm and (c2) 1.13 µm Al2O3, (d1) 0.2 µm and (d2) 1.48 µm AlN, (e1) 0.1 µm and (e2) 1.69 µm TiO2, (f1) 0.3 µm and (f2) 2 µm α-Ta2O5. The thickness of the Al substrate is fixed as 0.2 µm. And the permittivities and the corresponding energy-loss function of SiO2 (a3), Si3N4 (b3), Al2O3 (c3), AlN (d3), TiO2 (e3), and α-Ta2O5 (f3). The energy-loss functions for Si3N4 are multiplied by 10 for a better view of the curves. Dashed vertical lines show the peaks of energy-loss function and the corresponding Berreman wavelengths.

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Here, we demonstrate coupling to the Berreman modes at mid-IR wavelengths in thin layers of the polar materials, as depicted in Fig. 1(a1-f1). The numerically calculated p-polarized reflective spectra from SiO2/Al bilayer structure with SiO2 thickness of t = 0.1 µm are shown in Fig. 1(a1). A pronounced reflective minimum is occurred at highly off-normal incidence near the LO phonon wavelength of SiO2. These spectral features correspond to the coupling to the Berreman mode. For the thicker SiO2 with thickness of t = 0.74 µm (Fig. 1(a2)), we still observe a Berreman mode close to the LO phonon wavelength, but at a lower incident angle. This is compatible with the result from Eq. (1). Meanwhile, we also observe absorption from the TO phonon polariton in thicker SiO2, due to the longer optical path length of the light reflected and forth in thick film, which results in a strong and omnidirectional absorption. Similar results are shown in ENZ-Al bilayer structures consist of the other five ENZ materials (Fig. 1(b-f)). It should be noted that α-Ta2O5/Al bilayer structure exhibits two angle-dependent absorptance peaks located near 11.07 and 12.37 µm, which are corresponding to the Berreman modes excited in the α-Ta2O5 film (Fig. 1(f1)). For a much thicker α-Ta2O5 with thickness of t = 2 µm (Fig. 1(f2)), Berreman modes blue-shift lightly and occur at a lower incident angle. The above results are consistent with Eq. (1). The broadband omnidirectional high absorptance in 8−13 µm is due to the intrinsic absorption in α-Ta2O5.

To enable high absorption of both s- and p-polarized light, we transfer the flat ENZ films onto a structured surface. In this work, we proposed a structured surface consisted of a periodic array of pyramids and inverted-pyramids with a heigh of H, a base length of L, and a tilted angle θ (as shown in Fig. 2(a, b)). Considering the practical wet-etching of silicon, the tilted angles of pyramid and inverted pyramid unit-cell are both approximately 54.7°. Numerical simulations were performed by a commercial software package (ANSYS Lumerical FDTD) [33] utilizing finite difference time domain (FDTD) methods, the schematics of the corresponding simulated model are shown in Fig. 2(a, b). The simulation region geometry is symmetrical in the xy-plane, so in TM-polarization the boundary condition is chosen to be symmetric along the x-axis and anti-symmetric along the y-axis for faster simulation. The boundary condition along the z-directions is taken as a perfect matched layer (PML). We calculated the absorptivity (A) as follows: A = 1−RT, with R being the reflectivity and T being the transmittance. The thickness of the Al ground plane is larger than the skin depth of electromagnetic waves in the infrared regime, and will block any light transmitted, leading to nearly zero transmittivity in the range of interest. In the following simulation and discussion, the transmittance is set to zero, and we calculated the absorptivity (A) as follows: A = 1−R.

 figure: Fig. 2.

Fig. 2. (a) Schematic of the periodic array of pyramid patterned silicon substrate and the corresponding FDTD simulated model of the structured ENZ films. (b) Schematic of the periodic array of inverted-pyramid patterned silicon substrate and the corresponding FDTD simulated model of the structured ENZ films.

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3. Results and discussion

The numerical calculated absorption from a thin SiO2 film (t = 0.2 µm) grown on Al ground plane at an incident angle of α = 54.7° is shown in Fig. 3(a). As depicted in Fig. 3(a), when illuminated at p-polarized oblique incidence, the maximum absorption occurs at the wavelength of λB = 8.15 µm, at which the Berreman mode is excited. The Berreman wavelength (λB = 8.15 µm) is at the left side of LO phonon wavelength of SiO2 (λLO = 8.26 µm), which is consistent with the dispersion relation of Berreman mode [27].

 figure: Fig. 3.

Fig. 3. (a) Simulated p-polarized reflection and absorption for flat 0.2 µm SiO2 on Al at an incident angle of α = 54.7°. (b) Simulated TM-polarized absorption for 0.2 µm SiO2 on Al-coated pyramid patterned silicon substrate with a base length of L = 4 µm, a period of P = 6 µm, and a tilted angle of θ = 54.7°. (b) Simulated TM-polarized absorption for 0.2 µm SiO2 on Al-coated inverted pyramid patterned silicon substrate with a base length of L = 4 µm, a period of P = 6 µm, and a tilted angle of θ = 54.7°. The vertical black dashed line represents the wavelength of ENZ mode.

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In contrast to the flat Berreman-supporting ENZ film (Fig. 3(a)), when the same film is deposited on the patterned silicon substrate, several significant modifications are observed (Fig. 3(b, c)). When illuminated at TM-polarized normal incidence, both pyramid and inverted-pyramid structured ENZ films results in two absorption peaks, one of which is slightly offset from the Berreman wavelength with a wavelength of 8.42 µm (marked as vertical black dashed lines in Fig. 3(b, c)). This slight difference in absorption peak wavelengths between the flat Berreman-supporting ENZ film and structured ENZ film is a result of the different excitation conditions of the Berreman and ENZ modes. The structured ENZ films can couple the ENZ mode to free-space even at normal incidence, which is a result of scattering from the periodic pyramid structures that provides an additional momentum necessary to couple to the ENZ mode. The cross-section field profiles of electric field (|E|) and z-oriented electric field (Ez) at the ENZ modes for the pyramid and inverted-pyramid structured ENZ films are provided in Fig. 4(a, b) and Fig. 4(c, d), respectively. At the ENZ mode (λ = 8.42 µm) of the pyramid structured ENZ film, a strong confinement of the electric field is observed within SiO2 layer, which has a similar character with the dipole resonance. While for the inverted-pyramid structured ENZ film, the electric field is concentrated at the corner of the SiO2 layer (Fig. 4(c)), which leads to a decrease of the overlap between the electric field and the SiO2 layer. The strong confinement of the electric field within SiO2 contributes to the enhanced absorption in SiO2 at the ENZ mode. Accordingly, the absorption of pyramid structured ENZ film at the ENZ mode is much larger than that of inverted-pyramid structured ENZ film (Fig. 3(b, c)).

 figure: Fig. 4.

Fig. 4. (a, b) The field profile of electric field (|E|) and z-oriented electric field (Ez) of ENZ mode at the wavelength of λ = 8.42 µm for pyramid patterned silicon substrate. (c, d) The field profile of electric field (|E|) and z-oriented electric field (Ez) of ENZ mode at the wavelength of λ = 8.42 µm for inverted pyramid patterned silicon substrate. The tilt angle is θ = 54.7°, the period is P = 6 µm, and the base length is L = 4 µm.

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As demonstrated in previous works that the Berreman and ENZ modes are excited slightly above and below the plasma frequency in polaritonic film, respectively, with the offset between Berreman and ENZ modes dependent upon the film thickness. And the ENZ mode dispersion relation can be approximately written as [28]

$$\omega \approx {\omega _\textrm{p}}({1 - \beta {k_\parallel }t} )- i\frac{\gamma }{2}$$
where β is a coefficient that depends on the permittivities of the media above and under SiO2 film, t is the thickness of SiO2 film, ωp is the ENZ frequency of SiO2, γ is the damping frequency.

To further confirm the absorption near the LO phonon wavelength shown in Fig. 3(b) is the result of ENZ mode excitation, Fig. 5(a) and (b) shows the simulated TM-polarized absorption spectra for SiO2 on Al-coated pyramid patterned silicon substrate under the variation of the SiO2 thickness and period, respectively. According to the simulated results, the increment of the SiO2 thickness leads to a red-shift of the absorption peaks accompanied with an enhancement of absorption efficiency. Increment of the period leads to a blue-shift of the absorption peak, which is corresponding to a blue-shift of the absorption peaks with the decrease of transverse wave vector k|| (= 2π/P). As expected, the simulated results from Fig. 5(a, b) are consistent with the dispersion relation of ENZ mode as depicted in Eqs. (2).

 figure: Fig. 5.

Fig. 5. (a) Simulated TM-polarized absorption spectra for SiO2 on Al-coated pyramid patterned silicon substrate as a function of SiO2 thickness, with a fixed base length of L = 6 µm and a period of P = 6 µm. (b) Simulated TM-polarized absorption spectra for 0.2 µm SiO2 on Al-coated pyramid patterned silicon substrate as a function of the period. The blue dashed curves are guides to eye for indicating the ENZ mode varying with SiO2 thickness t and transverse wave vector k|| (= 2π/P).

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To explore the origin of another resonant absorption peak near the wavelength of 6 µm, we calculated the field profile of z-oriented electric field (Ez) at λ = 6.1 µm for pyramid structured ENZ film (Fig. 6(b, c)) and the field profile of z-oriented electric field (Ez) at λ = 6.12 µm for inverted-pyramid structured ENZ film (Fig. 6(e, f)). It is visible that the z-oriented electric field (Ez) shows a character of surface wave with an enhancement of the electric field between adjacent units, which exhibits a diffraction nature of resonance (named diffractive mode). This diffractive resonant feature can be also confirmed by the spectral shift with the periods of array. As shown in Fig. 7(a), the diffractive mode (labeled as Roman numerals) is red-shifted with the increase of the period P, which indicates as a diffractive resonant feature.

 figure: Fig. 6.

Fig. 6. (a) Cross-section schematic diagram for pyramid structured ENZ film. (b, c) The field profile of z-oriented electric field (Ez) of diffractive mode at λ = 6.1 µm for pyramid structured ENZ film over two orthogonal cross sections, yz (b) and xy (c), respectively. (d) Cross-section schematic diagram for inverted-pyramid structured ENZ film. (e, f) The field profile of z-oriented electric field (Ez) of diffractive mode at λ = 6.12 µm for inverted-pyramid structured ENZ film over two orthogonal cross sections, yz (e) and xy (f), respectively. The tilted angle is θ = 54.7°, the period is P = 6 µm, and the base length is L = 4 µm for both patterned surfaces.

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 figure: Fig. 7.

Fig. 7. (a) Simulated TM-polarized absorption spectra for 0.2 µm SiO2 on Al-coated pyramid patterned silicon with a fixed base length of L = 4 µm and a varied period of P. (b) Simulated TM-polarized absorption spectra for 0.2 µm SiO2 on Al-coated pyramid patterned silicon with a fixed period of P = 6 µm and a varied base length of L. The tilted angles in (a) and (b) are both 54.7°. (c) Simulated TM-polarized absorption spectra for 0.2 µm SiO2 on Al-coated pyramid patterned silicon with fixed period and base length of P = L = 6 µm as a function of tilted angle θ.

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As can be seen from Fig. 7(a-c), the structural parameters of the structured surface have significant effects on the absorption spectra. Figure 7(a) illustrates the interaction between the ENZ mode and diffractive mode and resulting in spectral narrowing as the period increases. Indeed, such Fano-like mode interactions have been reported in a broad range of periodic arrays of polaritonic resonators, known as collective resonances or surface lattice resonances [34,35]. To avoid the interaction of the diffractive and ENZ modes, the period of the structured surface is designed to be smaller than the ENZ wavelength of the ENZ film. For the case shown in Fig. 7(b) with a constant period of P = 6 µm and a varied base length L, the diffractive and ENZ modes both maintain the constant wavelengths, and the absorption of ENZ mode increases with the base length L. A similar spectral tuning can be seen in Fig. 7(c), a significant broaden and enhanced absorption of the ENZ mode is occurred with the increase of tilted angle. Additionally, in Figs. 7(b) and 7(c), a relative weak absorption peak near the wavelength of 9.3 µm is the origin of the localized surface phonon polaritons (LSPhPs) in SiO2. As we discussed above, the increasing of the base length (L) and tilted angle (θ) enables more and stronger confined electromagnetic field within the SiO2, which results in an enhanced absorption of ENZ modes, as depicted in Fig. 7(b, c).

Based on the near-unity narrowband absorption resulting from the SiO2 on Al-coated silicon pyramid surface, the broadband and polarization-independent near-perfect absorption is possible by replacing the single-layered SiO2 with multilayered ENZ films. To validate this supposition, we exploit gradient ENZ materials to deposit on Al-coated silicon pyramid surface. The gradient ENZ materials are SiO2, Si3N4, Al2O3, AlN, TiO2, and α-Ta2O5. The simulated TM-polarized absorption spectra for the system of single-layered ENZ material with the thickness of 0.1 µm deposited on Al-coated silicon pyramid surface are shown as color dashed curves in Fig. 8. They exhibit single-band absorption characteristics near the corresponding Berreman wavelength of ENZ materials. When these single-layered ENZ materials are stacked to form multilayered ENZ films, the simulated TM-polarized absorption spectrum exhibits a wideband absorption in the range from 8 µm to 14 µm (black solid curve in Fig. 8).

 figure: Fig. 8.

Fig. 8. Simulated TM-polarized absorption spectra for multilayered ENZ films (black solid curve) and single-layered ENZ film (color dashed curves) on Al-coated pyramid patterned silicon substrate. The parameters are L = 6 µm, P = 6 µm, θ = 54.7°. The thicknesses of each layer in single-layered and multilayered ENZ films are all 0.1 µm.

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To enable broadband and near-perfect absorption, the optimized design of multilayered ENZ films is obtained with the thicknesses of 0.306 µm SiO2, 0.201 µm Si3N4, 0.449 µm Al2O3, 0.5 µm AlN, 0.5 µm TiO2, 0.5 µm α-Ta2O5. The simulated absorptive spectra of the optimized flat multilayered ENZ films and structured multilayered ENZ films are shown in Fig. 9. It should be noted that in the short-wavelength region, the average absorption of structured ENZ films is much higher than that of flat ENZ films, with an appearance of two new absorption peaks at the wavelength of λSPP = 7.11 µm and λGM = 7.74 µm, respectively.

 figure: Fig. 9.

Fig. 9. The simulated absorption spectra of the optimized flat multilayered ENZ films at an incident angle of 54.7° (black curve) and optimized structured multilayered ENZ films at normal incidence (red curve). The tilted angle θ = 54.7°, the period P = 6 µm, the base length L = 6 µm.

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To better understand the physical mechanism of the two absorption peaks at λ = 7.11 µm and 7.74 µm, we calculated the field distributions at the corresponding resonance wavelength. Figure 10(a) depicts the electric field at the wavelength of 7.11 µm, an enhanced electric field occurs near the metal surface and the field decays in the ENZ materials away from the metal surface, indicating the excitation of the surface plasmon polariton (SPP), which is a grating-induced surface wave mode. The representative y-oriented magnetic field profile for resonant absorption at the wavelength of 7.74 µm demonstrates the guided-mode nature of the resonance (Fig. 10(d)).

 figure: Fig. 10.

Fig. 10. (a, b) The field profile of electric field (|E|) and z-oriented electric field (Ez) of SPP mode at the wavelength of λ = 7.11 µm. (c, d) The field profile of magnetic field (|H|) and y-oriented magnetic field (Hy) of guided mode at the wavelength of λ = 7.74 µm. The tilted angle is θ = 54.7°, the period is P = 6 µm, and the base length is L = 6 µm.

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In practical fabrication process, the tilted angle of the pyramids may vary with different wet-etch condition. We calculated the effect of tilted angles on the absorptive spectra of the structured ENZ films (Fig. 11(a)). It demonstrates that when the tilted angle is 0°, the total absorption results from phonon absorption in the multilayered ENZ materials. As the tilted angle increases to 30°, the enhanced absorption in short-wavelength region results from the excitation of SPP, guided mode, and ENZ mode. With further increasing of the tilted angle, the total absorption is significantly increased. We can conclude that the physical mechanism of the enhanced and broaden absorption is the combination of the SPP, guided mode, ENZ mode and the TO phonon polariton. The symmetric, pyramid shape of the structures also enables the coupling of both p- and s-polarized light to the free-space. The simulated absorptive spectrum of the optimized structured ENZ films under normal incidence (α = 0°) for different polarized angle ϕ is shown in Fig. 11(b), as can be expected, the absorptive spectrum exhibits a polarization-independent feature.

 figure: Fig. 11.

Fig. 11. (a) Simulated absorptive spectra of the optimized structured ENZ films varying with the tilted angle θ of the pyramid for TM-polarized (ϕ = 0°) and normal incidence (α = 0°). (b) Simulated absorptive spectra of the optimized structured ENZ films under normal incidence (α = 0°) for polarized angle ϕ of 0° and 45°. (c) Simulated absorptive spectra of the optimized structured ENZ films varying with incident angle for TM-polarization (ϕ = 0°). (d) Simulated absorptive spectra of the optimized structured ENZ films varying with incident angle for TE-polarization (ϕ = 90°). The structural parameters: tilted angle θ = 54.7°, period P = 6 µm, base length L = 6 µm.

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Moreover, a large-angle absorption is essential in many practical applications. As shown in Fig. 11(c, d), the structuring of the ENZ films results in an ultrabroadband near-unity absorption in the range of LWIR from near-normal incidence up to approximately 40° off-normal incidence, with an average absorption covering LWIR band over 95% for TM-polarization at an incident angle of 40° and over 92% for TE-polarization at an angle of 40°.

Finally, we point out three typical applications of the ultrabroadband wide-angle absorbers in the field of solar cell, thermal image, and thermal management. The ultrabroadband high-efficient absorption in LWIR enables day-time radiative cooling for solar cell, which can effectively cool the solar cells and avoid the failure of performance caused by overheating. Moreover, the patterned silicon substrates are also widely used for the solar energy absorption enhancement. Therefore, the ultrabroadband absorption structure proposed in this paper can be effectively compatible with the structural design of solar cells. In addition, the near-perfect broadband absorption covering the whole LWIR enables a much higher responsivity of the thermal imager. The patterned silicon substrate can be replaced with heat-sensitive materials (e.g., VOx and a-Si) and the metal layer can be used as an electrode, which makes our proposed absorber compatible with the fabrication process and structural design of bolometers. The low loss of ENZ materials and high reflection of Al in visible range might result in high solar reflectivity when illuminated from the ENZ materials side, while the high loss of silicon in visible and the light trapping effect in structured surface can result in an enhanced solar absorption when illuminated from the silicon side. With the combination of the high LWIR emissivity, the structured multilayered ENZ films are able to implement multifunctional passive thermal management and afford new possibility for energy conservation solution.

4. Conclusion

In summary, we have proposed an ultrabroadband metamaterial-based absorber composed of multilayered ENZ films grown on a metal-coated patterned silicon substrate. The ultrabroadband near-perfect absorption results from the combination of four mechanisms, namely SPP, guided mode, ENZ mode and TO phonon polariton. The symmetric, pyramid shape of the patterned silicon substrate enables the coupling of both p- and s-polarized light to free-space, resulting in a polarization-independent absorption. Besides, our proposed device also enables wide-angle and wideband absorption in both polarizations. Here our report proposes an alternative approach to realize broadband and wide-angle absorption. Moreover, the designed absorber possesses a lithography-free, cost-effective, and easy-to-fabricate structure, and is compatible with the fabrication process of commercial solar cells and bolometers, which offers an opportunity for applications in radiative cooling of solar cell and thermal image.

Funding

National Natural Science Foundation of China (62171079); Natural Science Foundation of Sichuan Province (2022NSFSC0041).

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No.62171079), and Natural Science Foundation of Sichuan (No.2022NSFSC0041).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (11)

Fig. 1.
Fig. 1. Simulated p-polarized reflective spectra varying with incident angle and wavelength for ENZ films with different thickness on aluminum (Al) substrate, (a1) 0.1 µm and (a2) 0.74 µm SiO2, (b1) 0.2 µm and (b2) 0.5 µm Si3N4, (c1) 0.2 µm and (c2) 1.13 µm Al2O3, (d1) 0.2 µm and (d2) 1.48 µm AlN, (e1) 0.1 µm and (e2) 1.69 µm TiO2, (f1) 0.3 µm and (f2) 2 µm α-Ta2O5. The thickness of the Al substrate is fixed as 0.2 µm. And the permittivities and the corresponding energy-loss function of SiO2 (a3), Si3N4 (b3), Al2O3 (c3), AlN (d3), TiO2 (e3), and α-Ta2O5 (f3). The energy-loss functions for Si3N4 are multiplied by 10 for a better view of the curves. Dashed vertical lines show the peaks of energy-loss function and the corresponding Berreman wavelengths.
Fig. 2.
Fig. 2. (a) Schematic of the periodic array of pyramid patterned silicon substrate and the corresponding FDTD simulated model of the structured ENZ films. (b) Schematic of the periodic array of inverted-pyramid patterned silicon substrate and the corresponding FDTD simulated model of the structured ENZ films.
Fig. 3.
Fig. 3. (a) Simulated p-polarized reflection and absorption for flat 0.2 µm SiO2 on Al at an incident angle of α = 54.7°. (b) Simulated TM-polarized absorption for 0.2 µm SiO2 on Al-coated pyramid patterned silicon substrate with a base length of L = 4 µm, a period of P = 6 µm, and a tilted angle of θ = 54.7°. (b) Simulated TM-polarized absorption for 0.2 µm SiO2 on Al-coated inverted pyramid patterned silicon substrate with a base length of L = 4 µm, a period of P = 6 µm, and a tilted angle of θ = 54.7°. The vertical black dashed line represents the wavelength of ENZ mode.
Fig. 4.
Fig. 4. (a, b) The field profile of electric field (|E|) and z-oriented electric field (Ez) of ENZ mode at the wavelength of λ = 8.42 µm for pyramid patterned silicon substrate. (c, d) The field profile of electric field (|E|) and z-oriented electric field (Ez) of ENZ mode at the wavelength of λ = 8.42 µm for inverted pyramid patterned silicon substrate. The tilt angle is θ = 54.7°, the period is P = 6 µm, and the base length is L = 4 µm.
Fig. 5.
Fig. 5. (a) Simulated TM-polarized absorption spectra for SiO2 on Al-coated pyramid patterned silicon substrate as a function of SiO2 thickness, with a fixed base length of L = 6 µm and a period of P = 6 µm. (b) Simulated TM-polarized absorption spectra for 0.2 µm SiO2 on Al-coated pyramid patterned silicon substrate as a function of the period. The blue dashed curves are guides to eye for indicating the ENZ mode varying with SiO2 thickness t and transverse wave vector k|| (= 2π/P).
Fig. 6.
Fig. 6. (a) Cross-section schematic diagram for pyramid structured ENZ film. (b, c) The field profile of z-oriented electric field (Ez) of diffractive mode at λ = 6.1 µm for pyramid structured ENZ film over two orthogonal cross sections, yz (b) and xy (c), respectively. (d) Cross-section schematic diagram for inverted-pyramid structured ENZ film. (e, f) The field profile of z-oriented electric field (Ez) of diffractive mode at λ = 6.12 µm for inverted-pyramid structured ENZ film over two orthogonal cross sections, yz (e) and xy (f), respectively. The tilted angle is θ = 54.7°, the period is P = 6 µm, and the base length is L = 4 µm for both patterned surfaces.
Fig. 7.
Fig. 7. (a) Simulated TM-polarized absorption spectra for 0.2 µm SiO2 on Al-coated pyramid patterned silicon with a fixed base length of L = 4 µm and a varied period of P. (b) Simulated TM-polarized absorption spectra for 0.2 µm SiO2 on Al-coated pyramid patterned silicon with a fixed period of P = 6 µm and a varied base length of L. The tilted angles in (a) and (b) are both 54.7°. (c) Simulated TM-polarized absorption spectra for 0.2 µm SiO2 on Al-coated pyramid patterned silicon with fixed period and base length of P = L = 6 µm as a function of tilted angle θ.
Fig. 8.
Fig. 8. Simulated TM-polarized absorption spectra for multilayered ENZ films (black solid curve) and single-layered ENZ film (color dashed curves) on Al-coated pyramid patterned silicon substrate. The parameters are L = 6 µm, P = 6 µm, θ = 54.7°. The thicknesses of each layer in single-layered and multilayered ENZ films are all 0.1 µm.
Fig. 9.
Fig. 9. The simulated absorption spectra of the optimized flat multilayered ENZ films at an incident angle of 54.7° (black curve) and optimized structured multilayered ENZ films at normal incidence (red curve). The tilted angle θ = 54.7°, the period P = 6 µm, the base length L = 6 µm.
Fig. 10.
Fig. 10. (a, b) The field profile of electric field (|E|) and z-oriented electric field (Ez) of SPP mode at the wavelength of λ = 7.11 µm. (c, d) The field profile of magnetic field (|H|) and y-oriented magnetic field (Hy) of guided mode at the wavelength of λ = 7.74 µm. The tilted angle is θ = 54.7°, the period is P = 6 µm, and the base length is L = 6 µm.
Fig. 11.
Fig. 11. (a) Simulated absorptive spectra of the optimized structured ENZ films varying with the tilted angle θ of the pyramid for TM-polarized (ϕ = 0°) and normal incidence (α = 0°). (b) Simulated absorptive spectra of the optimized structured ENZ films under normal incidence (α = 0°) for polarized angle ϕ of 0° and 45°. (c) Simulated absorptive spectra of the optimized structured ENZ films varying with incident angle for TM-polarization (ϕ = 0°). (d) Simulated absorptive spectra of the optimized structured ENZ films varying with incident angle for TE-polarization (ϕ = 90°). The structural parameters: tilted angle θ = 54.7°, period P = 6 µm, base length L = 6 µm.

Equations (2)

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h B = λ B 2 π cos α sin 2 α [ Im ( 1 ε ) | max ] 1
ω ω p ( 1 β k t ) i γ 2
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