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Abstract
We propose a design rule for broadband metamaterial absorbers and investigate their plasmonic properties under solar irradiation. The metamaterials consist of periodic arrays of titanium nitride (TiN) rings placed on an antireflective MgF2 dielectric film on a TiN bottom layer. We simulate the absorption of our metamaterials and find the dependence of the optical spectrum on structural parameters. From this, we propose a simple rule to design the nanostructures with an average spectral absorptivity greater than 95% over the solar spectrum from 200 to 3000 nm. Particularly, we introduce, for the first time, metamaterial perfect absorbers that can be designed using two-layer structures instead of higher-layer structures as conventional and sandwich designs. Our study would pave the way for great potential applications in the fields of solar energy harvesters and photo-to-thermal converters.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
To overcome the energy crisis that is restricting economic and social development, renewable energy is the primary solution. Solar energy is one of the cleanest and most abundant energy resources, which has been intensively studied to resolve the energy crisis. To effectively utilize solar energy, it is crucial to create novel structures with ultra-high and broadband absorption of light in the ultraviolet to near-infrared range (0.2-3.0 $\mu m$) [1–4]. The absorbed solar energy can be efficiently converted into heat to warm up objects and surrounding medium via the photothermal mechanism or into electricity via the photoelectric mechanism [1–4]. A wide range of different applications can be designed using these two mechanisms.
Metamaterials are artificial materials composed of subwavelength structures of metallic and dielectric materials arranged periodically [5,6]. They exhibit extraordinary electromagnetic properties that cannot be found in nature [5,6]. Over the past few years, there has been extensive research on metamaterial perfect absorbers with high absorption rates over a wide range of wavelengths [5,7–14]. The study of broadband metamaterial absorbers can lead to the development of efficient solar energy harvesters and photo-to-thermal converters to address the energy crisis. In general, noble metals like gold or silver have been widely exploited to fabricate metamaterials since plasmonic properties of these materials can enhance absorption by manipulating light-matter interactions [1–6,11]. However, the low melting point of noble metals limits their use in high-temperature applications [15–17].
Alternative plasmonic materials like transition metal nitrides (such as TiN) have recently been suggested to replace conventional materials [15–18]. TiN has several advantages including stable thermodynamic properties at high temperatures, simple fabrication, compatibility with standard silicon devices, and lower production costs [15–17]. Although titanium nitride has a similar optical spectrum to gold in the near-infrared and visible ranges, its real permittivity is smaller due to its lower carrier concentration. Furthermore, the optical properties of TiN can be easily adjusted by altering the processing conditions.
Scientists have proposed various types of ultra-high absorptivity solar absorbers based on TiN nanostructures. Liu [19], Mehrabi [20], Habil [21], and Zhong [22] designed ultra-broadband perfect solar absorbers based on stacked layers of TiN/TiO2 metasurfaces on a two-layered substrate. Meanwhile, Wu [23] proposed arrays of TiN and Si3N4 laminated ring structure on a three-layer substrate. Although this configuration achieves more than 90% absorption in the range of 280–300 nm and geometrical parameters can be optimized to obtain near-unity light absorption, their nanostructures become complicated with multilayers (more than four layers) and have multiple structural factors to control the absorption. The complexity of metamaterial structures could lead to high manufacturing costs and limit their potential applications. In other works, some sandwiched three-layer structures formed by an array of TiN rings [24–26] or cylinders [27,28] or cones [29]/dielectric layer/aluminum or TiN substrate have been investigated to attain perfect light absorption. Although these designs are simpler, the metamaterials only have nearly good absorption in the visible-to-near infrared band.
In a very recent work, Sun and his coworkers [30] also studied the structure of TiN nano-ring array, silica (SiO2) dielectric film, and TiN bottom layer and found that their metamaterials are perfect absorbers in the wavelength range from 300-2500 nm. They used the electric and magnetic field distributions to indicate that the plasmonic coupling leads to high absorption. Although structural sizes are tuned to understand how the variation affects the absorption spectrum, no specific guidelines are provided for creating ideal metamaterial absorbers. In addition, only a single configuration was found to attain an absorption rate of 95% for AM1.5 spectral radiation.
There are several questions not previously addressed: (i) can we propose a simple design rule to design many structures of broadband perfect absorbers? (ii) can the proposed broadband metamaterials become simpler? (iii) how does the plasmonic coupling modify optical absorption? In this study, we use the finite difference time domain (FDTD) method to resolve all questions mentioned above. A simple design rule is proposed to fabricate perfect solar absorbers. Based on the guidelines, we found many structures for ultra-broadband metamaterials that have an absorption rate greater than 92% in the whole spectral region.
2. Theoretical background
Our proposed broadband absorber has a metal–insulator–metal structure, as shown in Fig. 1, composed of a square lattice of ring-shaped TiN nanostructures on a magnesium fluoride (MgF2) dielectric layer thin film grown on a perfectly-reflective TiN substrate. The system can be experimentally fabricated using techniques described in Ref. [25,26]. The nanoring absorber was proved to exhibit higher absorption than the nanodisk and nanohole absorbers [26]. Here, we fixed the thickness of the bottom layer at 100 nm to mimic experiments in Ref. [25,26]. The structure is built using structural parameters: (1) a lattice period L = 430 nm as proposed in Ref. [30], (2) the height of the ring h1, (3) the inner and outer diameters of the TiN ring being d and D, respectively, and (4) the thickness of the MgF2 layer h2. To obtain the perfect metamaterial absorbers, we find D-d = 30 nm and h1 = D. Note that the penetration depth of TiN ($\delta = \lambda /(4\pi Im\left( {\sqrt {{\varepsilon_{TiN}}} } \right)$) approximately varies from 8 to 25 nm across the solar spectrum. Here, $\lambda $ and ${\varepsilon _{TiN}}$ are the wavelength and dielectric function of TiN, respectively. Consequently, when the thickness of the TiN ring is set to be 15 nm, it facilitates plasmonic coupling between inner and outer surfaces of the rings. This design rule suggests the number of decisive structural parameters reduces to 2 (h2 and D). We follow the structural design guidelines in our subsequent calculations.
Fig. 1. The ultra-broadband metamaterial based on periodic arrays of TiN ring placed on dielectric thin films of MgF2, and a TiN substrate.
There are several reasons why MgF2 is often preferred over SiO2 as the dielectric spacer layer in certain applications. First, MgF2 has a lower refractive index and this leads to less reflection and greater transmission of light through the structure [31,32]. Second, MgF2 has a wider transmission range in the UV region compared to SiO2 [31]. Third, the thermal conductivity of MgF2 (11.6 W/m/K) is much higher than that of SiO2 (1.38 W/m/K) [33]. Thus, MgF2 is more suitable for high-temperature devices. In other applications, one can consider SiO2 due to lower cost and higher chemical resistance.
We use FDTD solver in Computer Simulation Technology (CST) microwave studio software [34] to compute the absorption spectrum of the proposed metamaterial. The incident electromagnetic wave is a plane wave perpendicular to the surface. Its electric and magnetic components are parallel to the y-axis and x-axis, respectively. The open boundary condition is applied along the z-axis. Meanwhile, we employ the periodic boundary conditions along the x and y axes. The structure is excited using the Folquet port. The transmitter and receiver are positioned on opposite sides of the structure along the z-axis to determine the reflection and transmission coefficient. Then, the absorption A of broadband metamaterial absorbers is calculated by A = 1-R-T, where R and T are the reflectance and transmittance, respectively. The dielectric function of TiN and MgF2 are taken from Ref. [35] and [36], respectively. The dielectric function is a complex permittivity, which consists of a real part ($\varepsilon ^{\prime}$) and an imaginary part ($\varepsilon$). Figure 2 shows experimental data of the dielectric function of TiN and MgF2 as a function of wavelength [35,36]. The usage provides more accurate results than fixing the dielectric function of MgF2 to be constant.
Fig. 2. The real ($\varepsilon ^{\prime}$) and imaginary ($\varepsilon$) part of the dielectric function for (a) TiN and (b) MgF2 over wavelengths from 200 nm to 3000 nm.
To evaluate the effectiveness of our broadband metamaterials in collecting solar energy, we compute the average spectral absorptivity of the absorbers as
3. Results and discussions
Our calculations begin with the simplest structure which we assume h2 = 0. The three-layer sandwich structure becomes a two-layer system. Figure 3(a) shows the spectral absorbance of the absorber in the 200-3000 nm range as varying the outer diameter of the TiN ring. The wavelength range in our calculations is beyond the range of experimental dielectric data of TiN ($\lambda \le 2480$ nm) in Fig. 2, the validity of our absorption predictions within the wavelength range of 2480-3000 nm was confirmed in the Supplementary Materials. Remarkably, one can observe excellent broadband absorption in this solar spectral range. When the outer diameter of TiN rings is small (D $\le $ L/2), the plasmonic coupling among nanostructures is neglectable and, thus, the optical absorption of the metamaterials is not high. Increasing D from 240 nm to 340 nm significantly enhances the plasmonic coupling and harvests more sunlight in the solar spectral region. Numerical results in Fig. 3(b) clearly indicate that the mean spectral absorptivity grows from 88% to 95.2%. This suggests, for the first time, that it is possible to create perfect metamaterial absorbers using two-layered periodic plasmonic structures without a dielectric layer. As the size of TiN rings is increased further, the impact of the scattering process on the interaction between light and matter becomes more prominent, leading to a decrease in absorption. As a result, the mean absorption rate experiences a slight reduction from 95.2% to 92.2% with an increase in D from 340 nm to 400 nm.
Fig. 3. (a) Absorption spectra for systems having h2 = 0 at different outer diameters of TiN rings. (b) The average spectral absorptivity as a function of the outer diameter of TiN rings in the range of 240-400 nm.
The absorption mechanism in the TiN-based metamaterials originates from the interplay between localized surface plasmon resonance and the inherent loss of TiN. The real part of the dielectric function represents how a material responds to electric fields, while the imaginary part accounts for energy absorption and dissipation. When the real part of the dielectric function of TiN ($\varepsilon \mathrm{^{\prime}}$) is positive, as in the case of dielectric materials, the collective oscillation of electrons is dampened, and the localized surface plasmon resonance (LSPR) is less likely to occur. The incident light is slightly absorbed by the TiN nanoring layer. Thus, the contribution of the intrinsic loss of TiN (particularly, the bottom flat layer) to the absorption plays an important role. Meanwhile, when $\varepsilon \mathrm{^{\prime}}$ is negative as is the case for many metals ($\lambda \ge 462$ nm), the free electrons of TiN can collectively oscillate in response to the incident electric field, giving rise to LSPR. TiN has metallic properties and becomes an alternative plasmonic material. An increase in wavelength induces larger values of $\varepsilon \mathrm{^{\prime\prime}}$ and stronger light absorption. The electric field inside the TiN ring can be significantly enhanced due to cavity resonance. Meanwhile, the electric field is also tightly confined among the nanorings because of mutual interactions between the localized plasmonic resonances of neighboring nanostructures. The small thickness of the ring structure facilitates the interaction between the surface plasmons produced by the inner and outer TiN nanorings. As a result, the incident light is mainly absorbed by the nanoarray.
To have better understanding of physical mechanisms underlying the broadband perfect absorption of our metamaterials, we analyze the spatial distribution of electric and magnetic fields at $\lambda = 733$ and $1840$ nm, which are two resonance peaks of the two-layer systems having D = h1 = 340 nm, across a unit cell in Fig. 4. At a wavelength of 1840nm, the distribution of the electric field exhibits an electric dipole resonance within the upper ring antenna, whereas the magnetic field distribution does not appear significant. The magnetic field is largely absorbed by both the TiN flat layer and rings. Furthermore, the electric and magnetic field is strongly enhanced outside the TiN rings. This finding clearly indicates that the absorption is predominantly influenced by the plasmonic coupling among the TiN rings. Interestingly, at $\lambda = 733$ nm, this plasmonic coupling remains to intensify the electric field within the gaps between nanostructures but the cavity resonance also leads to a significant enhancement of the electric field inside the TiN rings. Thus, the high absorption performance is attributed to the strong cavity resonance and plasmonic interactions among plasmonic nanorings.
Fig. 4. (a) Electric and (b) magnetic field distribution at 733 and 1840nm in xz-plane for y = 0 nm.
Afterward, we conduct simulations to investigate how the thickness of the MgF2 spacer layer affects the absorption of the TiN-based metamaterials. Figure 5 shows the computed absorption spectra of our proposed absorbers for various h2 values. The metamaterials without the dielectric layer (h2 = 0) exhibit good light absorption in the visible region. However, in the longer wavelength region, the metamaterials have relatively low absorption. The presence of the MgF2 dielectric layer in the middle of two TiN layers can modify the resonances of the metamaterial structure and control over absorption peaks and bandwidth. This dielectric layer amplifies the electric field within the structure, enhances the interaction with incident electromagnetic waves, and thus increases the absorption performance. In addition, the dielectric layer can serve as an impedance-matching medium between the metamaterial and the surrounding environment. From this, the reflection can be minimized, and the absorption can be maximized. If these effects are compensated and mutually reinforcing, the absorption can be enhanced or remain unchanged. Numerical results in the mainframe of Fig. 5(a) reveal that the sandwiched three-layer structures with D = h1 = 240 nm significantly enhance the absorption in the near-infrared region as increasing the dielectric thickness. Particularly, the maximum absorption reaches 100% in the range of 800 nm to 1500 nm when h2 $\ge $ 60 nm. Because of the opposite absorption trends in two different light regimes, one can expect a non-monotonic variation of the average spectral absorption as the dielectric spacer layer thickness increases. Numerical results in the inset of Fig. 5(a) clearly confirm this analysis. For 60 nm $\ge $ h2$\ge $ 30 nm, ${\alpha _{solar}} \approx \textrm{}$93% and it suggests that our design rule allows us to find many structures having the same absorption and we can choose the best design for mass production.
Fig. 5. Absorption spectra for systems having (a) D = h1 = 240 nm, (b) D = h1 = 340 nm, and (c) D = h1 = 400 nm at different thicknesses of the MgF2 layer. The inset shows the average spectral absorptivity as a function of the thickness of the MgF2 layer.
To study how the MgF2 layer affects the optical absorption of the metamaterials having D = h1 = 340 nm, we carry out simulations and show results in Fig. 5(b). In the wavelength range from 200 nm to 2300 nm, the absorption band is lowered when the dielectric layer becomes thicker. Although the variation of the absorption band at higher wavelengths is reversed, the optical energy in this range is extremely small. Simulation results in the inset of Fig. 5(b) indicate that h2= 0 is an optimal structure parameter for our proposed broadband metamaterials. ${\alpha _{solar}}$ monotonically decreases with increasing h2. Adding the MgF2 layer slightly modifies the absorption as h2 $\le $ 30 nm and moderately decreases the light energy harvesting efficiency as h2 > 30 nm. Consequently, the two-layered metamaterial is not only the simplest structure but also the strongest absorption over the spectral range.
We compute the absorption spectra for metamaterials having D = h1 = 400 nm at different values of h2 and show results in Fig. 5(c). When the wavelength is less than 1600 nm, the absorption spectrum remains nearly unchanged with varying thicknesses of the MgF2 layer. The percentage of absorbed energy in the solar region (0.2–3 $\mu m$) fluctuates non-linearly from 91.3% to 93.25% for dielectric layer thicknesses less than 100 nm as shown in the inset of Fig. 5(c). Thus, it is possible to design ultrawideband solar energy absorbers performing similar photon-to-heat conversion efficiency.
Altering the distance between the inner and outer surface of TiN rings has a significant impact on optical absorption. To study how the thickness of the ring affects the energy harvesting systems, we perform simulations by setting D = h1 = 340 nm and h2 = 0 and changing the inner radius of TiN rings. The predicted spectral evolution is shown in Fig. 6(a). An increase in TiN ring thickness enhances optical absorption over the UV and visible range of 200 to 800 nm but weakens absorption bands in the near-infrared range. Thus, the average absorption rate in the spectral range exhibits a non-trivial change as the thickness of the TiN rings varies (seen in Fig. 6(b)). The maximum percentage of absorbed energy occurs when D-d = 30 nm. This result confirms that D-d = 30 nm is the optimal geometric parameter in our proposed design. At this size, the ring structure is sufficiently thin to enable the surface plasmon on the inner and outer surfaces of the ring to maximally couple with each other. However, increasing the thickness of the ring reduces the coupling between the electric field inside and outside the ring, and also leads to a decrease in the percentage of absorbed energy.
Fig. 6. (a) Absorption spectra for systems having h2 = 0 and D = h1 = 340 nm at different TiN-ring thicknesses. (b) The total solar absorptance as a function of the thickness of TiN rings in the range of 20-100 nm.
It is known that the incident angle has a strong effect on the absorption of structures [19,22,25,28]. In Fig. 7, we calculate the absorption spectrum of the two-layer metamaterials having D = h1 = 340 nm at different incident angles from 0° to 80°. The incident angle is determined by the angle at which the incident wave vector intersects with the surface normal of the metamaterials. In the LSPR region ($\lambda \ge $ 462 nm), an increase in the incident angle leads to a decrease in absorption. There are several reasons to explain the optical variation. First, at normal incidence, the incident light is perpendicular to the surface, the electromagnetic field penetrates the metamaterial more effectively and interacts with a large area of the TiN rings. This maximizes the chance of light absorption. As the incident angle increases, the effective area of interaction between the incident light and the TiN rings decreases. Second, at a shallower angle, the light travels through a longer path of the material. The elongated path means that the light has more opportunities to scatter, reflect, and transmit rather than being absorbed. Third, the orientation of the electric field changes. Thus, the efficiency of coupling with the resonant modes of the metamaterial is reduced and the interaction between the light and the TiN rings is weakened. Fourth, the resonance conditions can be shifted. The mismatch between the incident light's frequency and the metamaterial's resonance frequency can decrease absorption efficiency.
Fig. 7. Absorption spectra for systems having h2= 0 and D = h1 = 340 nm at different incident angles.
To compare the structural design and absorption efficiency of our proposed metamaterials with previous studies, we calculate the average absorption by
Table 1. TiN-based broadband metamaterial absorbers with different designs and their absorption performance
4. Conclusion
We have proposed a design rule for perfect metamaterial absorbers operating over the spectral region from 200 nm to 3000 nm. The structure consists of three layers including a TiN bottom film, a MgF2 dielectric film, and a square lattice of TiN nanorings. Our designs are based on three rules including the ring thickness equal to 15 nm, the height of TiN rings equal to the outer diameter of TiN rings, and the outer diameter of TiN rings larger than half of a lattice period to have plasmonic coupling. The proposed solar absorber shows promising energy absorption capability in the AM1.5 radiation spectrum with a ratio of 95.2%. Many structures can be found to have a solar absorption rate larger than 92%. Remarkably, a novel absorber structure based on two-TiN layers provides the best optical absorption. The dielectric layer is for designing ultra-wide perfect absorbers. Similar impedance matching conditions have also been employed for perfect transmission using metasurfaces [37]. Previous absorbers have been fabricated using standard electron-beam lithography techniques, with some examples of direct laser inscription [38]. These approaches could also be used to experimentally realize the absorbers demonstrated here, while shadow sphere lithography is another potential method of fabricating such ring structures of TiN [26]. The findings of this research would pave the way for the advancement and utilization of solar collectors and thermophotovoltaics.
Funding
POSCO (POSCO-POSTECH-RIST Convergence Research Center); Vietnam Academy of Science and Technology (KHCBVL.05/22-23); Institute for Information and Communications Technology Promotion (2019-0-01906); National Research Foundation of Korea (NRF-2022M3C1A3081312).
Acknowledgments
This research is funded by Vietnam Academy of Science and Technology under grant number KHCBVL.05/22-23. J.R. acknowledges the POSCO-POSTECH-RIST Convergence Research Center program funded by POSCO, and the National Research Foundation (NRF) grant (NRF-2022M3C1A3081312) funded by the Ministry of Science and ICT (MSIT) of the Korean government. T.B. acknowledges the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant (No. 2019-0-01906, the POSTECH Artificial Intelligence Graduate School program) funded by the MSIT of the Korean government, and the POSTECH PIURI fellowship.
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.
Supplemental document
See Supplement 1 for supporting content.
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