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Abstract
Ideal ultraviolet-visible-infrared (UV-VIS-NIR) absorbers with consistent performance at elevated temperatures and severe climate conditions are crucial to harvest energy for solar-thermophotovoltaic systems (STPVs). As solar energy promises to fulfill the power demands, its efficient utilization through high-performing light-absorbing devices is inevitable. The requirement of high-temperature durability makes conventional plasmonics an infeasible choice, and those highly thermostable refractory metals/their derivatives suitable ones. In this work, a lossy refractory plasmonic material i.e. Zirconium-Nitride-based subwavelength, ultra-broadband, wide-angle, polarization-insensitive, and free-space impedance-matched metasurface absorber in a three-level Pythagorean fractal structure is demonstrated. A comprehensive investigative study is conducted with the successful attainment of more than 90% absorption between ∼ 500–900 nm with a peak of more than 98% at 655 nm. The mean absorption for wideband (200–2500 nm) is 86.01% and it is 91.37% for visible range. The proposed study provides an efficient choice of meta-absorbers for realizing highly efficient STPVs.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
Corrections
20 March 2024: A correction was made to an affiliation.
1. Introduction
A clean, renewable energy i.e. solar energy, an alternative to fossil fuels, is being investigated as it is a major source of energy in light of the ever-increasing demand for power [1]. The sun is most reliable form of renewable energy in the world, whose energy is conventionally utilized with the help of semiconductor Si cells, which results in limited efficiency. To exceed the limit, solar energy is captured using a promising alternative i.e. Solar thermal photovoltaics (STPV) systems for power generation [2,3]. STPV generates power by using heat transfer between hot and cool layers such that the Shockley and Queisser (SQ) limit of solar cells [4] is crossed [5]. The thermailization and transmission losses of the solar cells restrict the conversion efficiency to 30% for single-junction PV cells which is 41% for full concentration of sun [5]. However, the STPV system being a combination of broadband absorber with narrowband emitter is meant for absorbing different energy photons efficiently, by maintaining a significant temperature difference between them. The narrowband emitter emits a matched photon so that the PV cells are efficiently used for power generation. Theoretically, it has been demonstrated that the STPV efficiency exceeds the SQ limit, accomplishing 54% and 85% under un-concentrated [5] and completely concentrated [6] solar light, respectively.
A blackbody is a perfect and efficient absorber owing to its broadband absorption capability of the illuminating electromagnetic energy. Numerous research efforts so far have been successfully made in realization of high performance perfect nanostructured absorber designs for number of attractive applications as nanoscale fluidics [7], nanoscale heat-source [8], photodetectors [9], microbolometers [10], thermal imaging [11], sensing [12], thermal management [13] as well as solar energy harvesting [6,14–17]. The absorber should be capable of absorbing the solar energy from UV to near-infrared frequency, while simultaneously lowering the mid-infrared re-emissions [1]. It should be a high-temperature, chemically and mechanically stable device. In the past, carbon nanotube arrays due to the low refractive index [18], the gold and silver-based designs due to plasmon polaritons [19], photonic crystals [20] and metallic arrayed designs [21] for the effects including Bragg and Rayleigh resonances have been investigated for their absorption characteristics. Each design has its associated challenges as complex fabrication, low spectral selectivity, or low operating temperature, thus becoming unsuitable for STPV applications [15].
In the succession, metamaterials came to the upfront as a successful choice for developing the absorbers as they can control the electromagnetic (EM) waves over the whole range of EM-spectrum and offer unique and exotic features for manipulating incident wave at subwavelength level [11,22]. They are artificial materials formed in the past decades as competitors to conventional materials for meeting the challenges of high performance nano-photonics applications [23]. Many interesting EM phenomena such as anomalous refraction and reflection, superior plasmonic effects, enhanced or blocked backscattering, engineered dielectric resonances, tunability and reconfigurability [22] have been demonstrated. Metasurfaces (two-dimensional metamaterials) are a collection of nano-antennas formed by subwavelength periodic nanostructures of metals and dielectrics [24]. They are found in potential applications including holograms [25,26], color imaging [27], flat optical elements [28], optical vortex generators [29], giant optical chirality [30], electromagnetic shielding, stealth technology [31] and absorbers [32]. These applications are realized based on different sizes and geometries/ shaped of nano-resonators. The shapes are simple geometries or are made using complex fractals, where fractals have a hierarchical structure inherent due to their recursive nature. They posses self-similar structures pattered to achieve desired response, offering higher degree of freedom resulting in resonances from each single element [33]. They enjoy this feature due to multiscale geometry involved in their design, thus becoming an ideal candidate for ultra-broadband behavior. Their design calls for a multimodal engineering to decide upon their order, as with higher fractal order, increased number of modes are excited inside fractal whose coupling eventually leads to have broadband result. They in general are quite complex and pose fabrication challenges, for example, Minkowski [34], Sierpiński fractal [35], Square Sierpiński carpet fractal [36], Fractal-cross absorber [37] and Cayley-tree fractal [38]. However, Pythagorean-tree is a plane fractal, simpler in design, and is composed of patches of small squares iterating in N-levels [39]. In an earlier work, the Pythagorean fractal has been employed for terahertz absorption [40]. With a view to broaden the bandwidth of metamaterial absorbers, continuous efforts are being keyed in by employing the stacked structures [41], or co-planar design of various resonant cells [42], or by adding lumped elements [43] or by using inherent high loss in dielectrics or semiconductors [44] over different frequency ranges [45].
Metasurface perfect absorbers with deeply subwavelength structure patterned in various topologies have drawn a lot of attention since their invention in 2008 by Landy’s group [46], which opened the routes for designing simple narrow as well as wideband absorbers. Metasurface absorbers employing different materials and structures like dense nanorods [47], nanotube films [48], planar multilayer photonic structures [49] and photonic crystals [50] have been so far being explored. In the same way, the simple MIM absorbers including Ti-SiO2-Al with > 90% average absorption for 354-1066 nm [51], an ultra-broadband (300-2000nm), polarization and angle-insensitive W-SiO2-W absorber with mean absorption of 91.7% [52], a broadband Ag-SiO2-Ag absorber structured in trapezoidal patterns [53] and many more [54,55] have been presented. Although, silver and gold based designs have shown high absorption characteristics, but they are not usable for high temperature being soft, thermally and chemically instable [14]. Furthermore, they mostly absorb only a narrowband because of their intrinsic reliance on plasmon resonances. These significant limitations might be mitigated by using refractory plasmonic materials, strengthening the progressing STPV technology as high-temperature forbearance, mechanical, chemical stability of the constituent materials are direly needed [6]. ZrN is an example of refractory material, which proves to be an ideal candidate capable of maintaining its optical properties having stability for increased temperatures due to its high melting point of 2980 °C and low oxidation rate and high corrosion resistance [56].
In this work, we have presented a broadband, ultrathin, polarization-independent, wide-angle metasurface absorber based on a high temperature stable refractory metal-nitride for optical and near-infrared regions. The proposed design is Pythagorean fractal in metal-insulator-metal (MIM) topology with three levels and has > 90% absorption in 498–917 nm with peak value of 98.38% at 655 nm. The mean absorption attained over 200–2500 nm is 86.01% while that of 91.37% in visible region from 400–800 nm for third level. The peak and mean averages for level 1 are 90.74% and 80.41%, and those for level 2 are 97.06% and 84.75%, respectively. The presented absorber exhibits stability up to 70° illumination angle with significantly high absorption efficiency. The presented design has been analyzed from macroscopic point-of-view too and it has shown perfect impedance matching resulting in a zero reflection at resonance. In addition, the polarization conversion ratio (PCR) for both transverse-electric and transverse-magnetic modes has been evaluated in terms of S-parameters leading to near-zero values. The presented design has been optimized in terms of all of its geometrical parameters. The materials for top resonator as well as the middle spacer layer have been compared with other metals and dielectrics respectively, in order to visualize the behavior of the structure with proposed ones. The design is symmetric, compact and simple to fabricate when compared to other complex fractal structure, has high absorptive characteristics over a wide range UV-VIS-NIR making the design distinguished from other broadband absorbers [34,37,38,40,57–59].
2. Design and simulation/ light matter interaction
Self-similar structures i.e. fractals offer an extra degree of freedom for altering the resonance frequencies and are an appropriate choice for ultra-broadband absorption devices. The proposed unit-cell has the MIM topology in Pythagorean fractal structure having x-y symmetry where each layer has its own role the in support of device absorption. The device is optimized by tuning the capacitance and inductance such that the impedance match takes place. ‘ZrN’ has been used because of its high loss and thermal stability when compared to other materials. The presented design is shown in Fig. 1 with its optimum dimensions including ground height of 150 nm, dielectric height of 60 nm and the top fractal height of 40 nm, with lattice constant of 300 nm and the squares in order are of sizes L × L, 4 L/5 × 4 L/5 and 2 L/5 × 2 L/5 with L = 86 nm. The proposed design in perspective view is shown in Fig. 1(a), whereas the level-wise front views are includes in Fig. 1(b-d). The full-wave simulations are carried out in the commercially available full-wave solver CST Microwave-Studio using periodic boundary conditions representing an infinite array. The total energy of light upon incidence is transmitted (T), reflected (R), and absorbed (A). The absorption A(λ,θ,φ) = 1–R(λ,θ,φ)–T(λ,θ,φ), where R(λ,θ,φ) = |S11|2 is reflectance and T(λ,θ,φ) = |S21|2 is transmission with S11 and S21 being reflection and transmission coefficients, respectively. The transmission is assured to be non-existent via metal ground plane whose thickness is made greater than the skin depth, thus making A(λ,θ,φ) = 1–R(λ,θ,φ).
Fig. 1. (a) Pythagorean fractal ZrN broadband absorber metasurface and its unit cell with incident EM waves with MIM topology having L × L, 4 L/5 × 4 L/5 and 2 L/5 × 2 L/5 sizes in succession, respectively. The ground plane with height 150 nm, spacer with height 60 nm and the top fractal structure with height 40 nm, with period of 300 nm and L equal to 86 nm. (b) Fractal level-1 (c) Fractal level-2 and (d) Fractal level-3.
3. Results and discussion
3.1 Level-wise absorption for fractal structure
The absorption behavior for each fractal level obtained through full-wave simulations over 200–2500 nm, covering UV-VIS-NIR domains, is shown in Fig. 2(a), where the maximum values realized for level-1 and level-2 respectively are 90.74% and 97.06%. The average values over the broad range for these levels are 80.41% and 84.75%, respectively while the broadband absorption is obtained when all of fractal orders are combined to form a supercell. The device has been simulated for both TE- and TM-polarizations where the wideband transmission, reflection and absorption spectra are shown in Fig. 2(b), indicating polarization insensitivity. It is evident that the absorption is higher whose peak exists in visible regime at 655 nm. The highest value obtained for third level fractal is 98.38% with a broadband average of 86.01%. We observe that absorption values remain above 90% in 498–917 nm and are above 80% in the region 200-1090 nm, respectively.
Fig. 2. (a) Level-wise absorption characteristics of design sequence. (b) Absorption, transmission and reflection of level-3 Pythagorean fractal. (c) The constitutive parameters of the proposed design retrieved from CST (inset from 200–600 nm showing resonant conditions where $\varepsilon = \mu $. (d) Normalized impedance of the proposed meta-atom.
3.2 Constitutive parameters and impedance matching
The goal for achieving the maximum absorption is equivalent to minimizing reflections at the interfaces and the assurance of destructive interferences of the multiple reflections inside the dielectric layer. The operation of an absorber is explained by homogenous material’s effective optical parameters i.e. the electric permittivity (ɛ) and the magnetic permeability (µ) from macroscopic EM perspective. At critical condition, resonance takes place for perfect impedance matching when R = 0 and both the effective parameters are same i.e. ɛ(ω) = µ(ω), indicating Z = Z0 in Fresnel equation of reflection given in Eq. (1) [39] resulting in highest absorption value [60,61].
3.3 Polarization conversion ratio (PCR)
The reflection coefficients used to determine the absorption i.e. S-parameters of the proposed absorber are shown in Fig. 3(a), where ${|{{S_{1,1}}(\omega )} |^2} = \; {|{{S_{2,2}}(\omega )} |^2} = R_1^2 = R_2^2$ & ${|{{S_{1,2}}(\omega )} |^2} = {|{{S_{2,1}}(\omega )} |^2} = T_1^2 = T_2^2$. All of them are seen to be insignificant as desired. The Polarization Conversion Ratio (PCR) is expressed in terms of these parameters using Eqs. (4) and (5), respectively for the transverse electric (PCR1) and transverse magnetic (PCR2) modes. The presented absorber has behaved same for both TE and TM waves, thereby making PCR close to zero as can be seen from Fig. 3(b).
3.4 Parametric sweep of geometrical parameters
It is a well-known fact that the metamaterial’s physical characteristics including effective permittivity (ɛr,eff) and effective permeability (µr,eff) depend on metallic resonator’s shape, material, and dimensions [23]. The thickness of each layer has a significant role in determining absorption magnitude. Further, the meta-atom structure's impedance is influenced by its physical parameters [62]. The consequences of geometric parameter modification on the absorption characteristics are shown in Fig. 4. As each of the parameters has a varied impact on how the absorption curve changes, each one of them has been used to tune the absorption behavior. The geometrical parameters of unit-cell including (L,p, hr, hs) are swept over a range to get the optimum absorption. ‘p’ is changed in a step of 10 nm from 300 to 350 nm (Fig. 4(a)), and is optimized as 300 nm. ‘L’ is changed from 76 to 86 nm with a step of 2 nm (Fig. 4(b)), and is optimized as 86 nm. Figure 4(c) demonstrates the change in absorption efficiency as a function of resonator’s height (hr) from 30 nm to 80 nm and it is observed that the resonance is red-shifted with increasing height. The change of the thickness of dielectric varies the capacitance and inductance values, which changes the absorption behavior. The height of spacer layer is varied between 40 and 80 nm and the performance maxima is achieved at 60 nm (Fig. 4(d)).
Fig. 3. (a) Co-polarization and Cross-polarized coefficient amplitudes in dB, and (b) PCR for the proposed structure in both TE and TM modes.
Fig. 4. Parametric analysis of geometrical parameters (a) lattice constant ‘p’ of the resonator, (b) square lengths ‘L’, (c) resonator height hr,(d) spacer (dielectric) height hs.
3.5 Performance comparison using different dielectrics and metals
The absorption performance is analyzed with different dielectric materials including aluminum oxide (Al2O3), gallium nitride (GaN), silicon nitride (Si3N4), amorphous hydrogenated silicon (a-Si:H) and aluminum nitride (AlN) for contrastive response from silica (SiO2). It can be observed from Fig. 5(a), that the best performance is realized in the case of SiO2 dielectric material. The average absorptions for the cases of Al2O3, GaN, Si3N4, a-Si:H, AlN and SiO2 are 73.32%, 70.53%, 81.39%, 76.31%, 74.76% and 85.99%, respectively. In addition, the relatively constant value of dielectric constant of silica and its thermal compatibility make this a favorable choice for application as spacer layer.
Fig. 5. The broadband absorption spectra comparisons. (a) The dielectric spacer replacement of silica with Aluminum oxide, Gallium nitride, silicon nitride, amorphous hydrogenated silicon and aluminum nitride with ZrN as design material. (b) The metal ground and nano-structure material replacement with silver, copper, tungsten and gold with silica as spacer. The design assumes the optimum dimensions for this analysis.
In addition, the proposed structure is studied using other materials than ZrN for its absorptive behavior. Silver (Ag), Tungsten (W), Copper (Cu) and Gold (Au) have been employed in the nanostructure and ground plane, where the results are plotted in Fig. 5(b). Here again, it is clearly seen that the results are in more favor of ZrN case. The average absorption values for Ag, Cu, W, Au and ZrN are 61.55%, 61.998%, 76.35%, 51.42% and 85.99% respectively. The difference is the absorption performance in different cases is described based upon Hagen-Rubens (H-R) relation [63]. According to H-R relation, a metal surface reflection is given by Eq. (6):
The highest absorption (1-R) takes place when the value of ‘k’ (imaginary part of optical constant) is higher than that of ‘n’ (real part of optical constant). The extinction coefficient value for ZrN is higher, thereby leading to have high intrinsic loss i.e. the absorption values because of reduced reflections [64]. For some metals, values of ‘n’ are also high resulting in weak absorption due to impedance mismatch even if the ‘k’ values are high.3.6 Incident angle stability
In context of real-time application, the feature of angle and polarization insensitivities play a key role [65–67]. The effect of incident as well as polarization angle on the spectra as function of wavelength for the optimized structure parameters has been studied where the results are plotted in Fig. 6 for both TE and TM polarization from 0° (normal) to 80° (non-normal). The fractal structure has lateral width symmetry so that polarization independence for normally incident light is exhibited. However, it can be seen that the average of the absorption undergoes a decrease with increase of incident angles. This happens because of longer path length for larger angles of incidence. The electric resonance mode is not excited effectively at larger angles due to reduced coupling accompanied with the reduced capability of wave confinement within spacer layer [16,68]. However, the presented design has enabled wide-angle insensitivity thereby exhibiting increased angular stability with polarization insensitivity. A lesser variation is observed for TM polarized light in comparison with TE polarized light (Fig. 6(a)), because the magnetic field can powerfully maintain the magnetic resonance strength at all incident angles while maintaining its direction at varying incident angles. Only a slight decrease is observed at larger wavelengths (Fig. 6(b)). The robustness is observed particularly up to 70° with highest value of 91.11% for TE and 97.52% for TM cases, respectively. The polarization angles are varied in (0° ≤ ϕ ≤ 90°), for which too a robust performance with very little change in values of absorption is observed as shown in Fig. 6(c).
Fig. 6. Angular dispersion from 0° to 80° of the absorbance peak for the polarized modes (a) TE, (b) TM and (c) for polarization angles from 0° to 90°.
3.7 E- and H-fields, surface current density
The electromagnetic field distributions gives an insight into the excitation of electromagnetic resonance phenomenon and their coupling which depicts the absorption mechanism, and therefore has been investigated for absorption explanation. The electric/ magnetic fields and the surface current distributions for two orthogonal polarizations at λ = 650 and 1500 nm have been presented in the x-y plane at z = 250 nm. It is clear from E-filed profiles in Figs. 7(a-d) that, the acquisition of opposite charges at the edges of the squares forming Pythagorean tree causes localized surface Plasmon excitation under the influence of E-field. In addition, the dielectric resonances takes place and induces additional surface plasmons for E-field enhancement. The EM power absorbed in a nonmagnetic material is given by equation. 7 [69]
with the angular frequency ω, ɛ” the imaginary permittivity, and $|E | $ the electric field amplitude. It is clear that the loss generated by localized resonances in ZrN nanostructures is significantly high to lead to a high absorption [14] throughout the entire working spectrum. In addition, the resonant dipolar moment confined in the dielectric spacer (SiO2) has assisted EM wave absorption. The H-filed profile for both TE and TM modes for the same wavelengths is shown in Figs. 7(e-h), and due to the structure symmetry, the H-field has the same distribution as that of E-field. The localized surface plasmons resonance has induced high H-field. The anti-parallel circulating current at resonator and ground layer interface comes from magnetic moment in the dielectric layer while reducing the reflections. At peak wavelength, the most dispersed surface is located which is 655 nm, whereas, a low surface charge exists at low absorption wavelengths (Figs. 7(i-l)).Fig. 7. Demonstration of (a–d) E-field (V/m) (e–h) H-field (A/m), and (i–l) surface current density (A/m2) of the presented absorber for TE and TM mode in 655 nm(max point) and 1500 nm (a min point) for z = 250 nm (max height of the nano-structure), each of which is show with scale bars.
3.8 Comparison of the proposed and other fractal designs
The comparison of the presented metasurface absorber has been given in Table 1 on the basis of the ranges of operation, the peak and average absorption, the material used to design them, their dimensions and the structure complexity. It can be seen that, most of the fractals are complex in their design and may pose difficulty in fabrication. In addition, many of the fractal structures operate in GHz and THz i.e. for longer wavelengths. However, the presented design adorned with the characteristics of broadband behavior, compactness, polarization independence, angle-insensitivity, high temperature stability, has a simple structure with being highly absorptive in nature.
Table 1. Comparative analysis of various metasurface based absorbers including plasmonic and refractory materials and of different fractal structures.
4. Conclusion
In summary, we have proposed three level Pythagorean fractal MIM absorber with ZrN-SiO2-ZrN meta-atom structure which is numerically studied for its use in solar energy harvesting application. The design makes use of the fascinating trait of fractals of frequency shifting characterized by N resonant peaks for an Nth-order structure. The nanostructured absorber with an overall thickness of 250 nm has exhibited wideband absorption behavior for UV-VIS-NIR regions. The structure optimization realized via different geometrical parameters variation results in tuning of constitutive optical parameters i.e. electric permittivity and magnetic permeability to exhibit resonance i.e. free space impedance matching thereby reducing the reflections, and eventually leading to higher absorption. Under normal incidence, the performance evaluation over the range 300–2500 nm administers level-wise peak absorption as 90.74%, 97.06%, and 98.38%, respectively, leading to conclude that most of the incident photons are absorbed owing to the fact that at resonance, the localized EM field is greatly amplified. The average absorption obtained for 200–2500 nm is 86.01% while it is 91.37% for the visible spectrum. In addition, the EM-field and surface current distribution profiles have been studied which leads to conclude that the absorption results from the power loss originated from the continuous electron transition upon incidence of light within the metal. The outstanding results indicate that the absorber presented in this research can be applied in any complicated electromagnetic scenario for any of the oblique incident angles for effectively absorbing solar energy. In addition, out of the fractals family the presented one is uniquely absorbing the visible spectrum while featuring the simple structure.
Funding
King Saud University (RSP2024R474).
Acknowledgement
The authors would like to acknowledge the support provided by Researchers Supporting Project number (RSP2024R474), King Saud University, Riyadh, Saudi Arabia.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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