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Abstract
A perfect absorber in the visible-infrared regime maintaining its performance at elevated temperatures and under a harsh environment is needed for energy harvesting using solar-thermophotovoltaic (STPV) systems. A near-perfect metasurface absorber based on lossy refractory metal nitride, zirconium-nitride (ZrN), having a melting-point of 2,980°C, is presented. The numerically proposed design with metal-insulator-metal configuration exhibits an average of > 95% for 400-800 nm and 86% for 280-2200 nm. High absorption is attributed to magnetic resonance leading to free-space impedance matching. The subwavelength structure is polarization- and angle-insensitive and is highly tolerant to fabrication imperfections. An emitter is optimized for bandgap energy ranging from 0.7 eV-1.9 eV.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials establish effective control of amplitude, phase, and polarization of EM waves [1]. Through this control, many exotic electromagnetic (EM) phenomena leading to potential applications, including but not limited to light-harvesting [2], thermoplasmonics [3], sensing [4], flat lenses [5], holography [6], and vortex beam generation [7], have been demonstrated using metamaterials. However, in the optical regime, metamaterials undergo severe fabrication challenges [8]. On the contrary, metasurfaces – planar metamaterial counterparts – composed of sub-wavelength periodic/ aperiodic elements provide an alternative to attain desirable functionalities through a less intricate fabrication process [9], resulting in remarkable miniaturization and integration of conventional optical components [10]. The metasurfaces find their major applications in the optical regime for wavefront manipulation (phase control) and absorbers/ emitters (amplitude control).
To utilize solar spectrum – an evergreen source of energy – the need for a broadband absorber in optical regime remains critically relevant [11,12] for thermal emission [13], color filtering [14], and harvesting solar energy [15]. Landy in 2008 first reported a triple-layer MIM (M = Metal; I = Insulator) metamaterial-based perfect EM absorber [16]. Plasmonic metamaterials exhibited a radical breakthrough in light-matter interaction: a gold-based plasmonic structure offered absorption of light in 240-550 nm range [17] while a silver-based plasmonic blackbody showed 90% absorption in 240-850 nm range [18]. Using the same topology, many absorbers have been demonstrated; however, they pose different challenges such as poor selectivity, complex fabrication process, and broad thermal radiation emissions at elevated temperatures. As such, broadband absorbers with the bandwidth (BW) in the range of the sun’s blackbody spectrum are still being designed and investigated for energy harvesting applications with enhanced conversion efficiencies [19]. Similarly, Aluminum- and Alkali metals-based absorbers have also been exploited [20,21], achieving efficiencies of above 90% for 500-1000 nm and above 80% for 500-550 nm, respectively. However, the high cost, poor thermal and chemical stabilities, and Complementary Metal-Oxide-Semiconductor (CMOS) incompatibility [22], hindered the widespread use of these metals for absorption applications.
A perfect solar absorber should absorb broadband omnidirectional radiations while enduring higher temperatures and resisting oxidation. Recently, refractory materials, providing plasmonic-like responses in the optical region [23], are explored as a competitor to conventional metals for absorber applications [10]. Another impressive feature of refractory materials, such as TiN, ZrN and HfN, is their tunability of plasmonic properties through nitrogen stoichiometry [10]. In comparison to metals, transition metal nitrides show superior mechanical properties [24], thermal stability, and CMOS compatibility [25]. TiN and ZrN, with respective melting points of 2930 °C and 2980 °C, are extensively investigated for electrical and optical applications, as they exhibit plasmonic properties, high electron conductivity, and mobility [26]. Zirconium Nitride (ZrN) has shown to behave metallically with low electrical resistivity [27,28]. It has the highest stability compared to other refractory metal nitrides [29], and can be grown by the process of heteroepitaxy on Si, whereas other metal nitrides are usually grown epitaxially on MgO and, in some cases, on sapphire. Also, it is compatible with electron affinities of Ga-rich InxGa1-xAs, and In-rich InxGa1-xP semiconductors [30]. Furthermore, the oxidation resistance of ZrN is also superior as compared to TiN [31]. In [32], a tandem structure using ZrN is shown to achieve 86% absorption. It outperforms TiN in near-field enhancement, and its small spherical nanoparticles outperform even gold at some frequencies for the applications of thermoplasmonics, photothermal therapy, photothermal imaging, and thermophotovoltaics [10], making it a perfect candidate for use in solar absorption.
In this work, a promising Refractory-metal-nitride Metamaterial Absorber (RMA) is proposed to realize an ultra-broadband and polarization-/ angle-insensitive solar absorber with a compact square ring structure employing ZrN. It is composed of MIM topology with the top nanostructure of ZrN minimizing reflections, the intermediate dielectric layer of SiO2 acting as Fabry-Pérot cavity to trap EM waves, and the bottom ground layer of ZrN blocking transmissions. The proposed absorber shows 86% average absorptance for a broadband range of 280-2200 nm and above 95% for 400-800 nm. Moreover, the design is robust to fabrication errors with a tolerance of ±10 nm, ±20 nm, ±30 nm and ±40 nm in each dimension with drop in peak absorption of only 0.19%, 0.26%, 0.34% and 0.64% respectively. Similarly, the design exhibits almost the same average absorption if the square shape were fabricated as a circular ring with the same dimensional tolerance of ±10 nm, resulting in the average absorption dropping from 95% to just 94.21%. Additionally, the proposed design is capable of preserving its performance in high-temperature environments due to an extremely small thermal expansion coefficient, which does not allow ZrN to register any significant variation in dimensions owing to temperature fluctuations [33].
2. Structure design and simulations
The numerical simulations of the structure are carried out using a commercially available full-wave solver – CST-MWS. The optical constant values for ZrN are taken from [34]. The optimization of the geometrical parameters is carried out using parametric sweeps in simulations followed by the PSO (Particle Swarm Algorithm) to optimize the geometry of the unit cell in order to achieve high absorption. The optimized parameters are obtained as : the unit cell period p = 300 nm, ground plane height hg = 150 nm, spacer height hs = 60 nm, length l = 125 nm, width w = 50 nm, and height h = 40 nm of ZrN ring, as shown in Fig. 1(a) The spacer layer of silicon dioxide (SiO2) is employed because of its fairly high melting point of ∼1600 °C, and low yet relatively constant refractive index for optical regime [35]. The absorption mechanism for a device governed by EM resonance is given by $A({\lambda },\theta ,\varphi )\, = \,1 - R({\lambda },\theta ,\varphi )\, - T({\lambda },\theta ,\varphi )$. The transmission is completely blocked by ground-plane and reflection is minimized by top layer, with the absorption being near-unity for entire visible range as ∼100% incident photons are absorbed (Fig. 1(b)), with an average A = 95% for 400–800 nm range. Figure 1(c) shows prominent anti-parallel surface currents in the top and bottom metal layers, which are attributed to strong magnetic resonances taking place in the proposed design. The excellent absorption properties show a great improvement in absorption spectrum when compared with other metallic nanoresonator-based absorbers.
Fig. 1. ZrN metasurface solar absorber. (a) Unit cell schematic repeating in x and y directions forming a square array with period p. (b) simulated absorption, reflection and transmission for ZrN-metasurface absorber for broadband range. (c) surface current of metamaterial absorber at peak absorption wavelength. The current flows towards right on the ring surface and towards left at the ground surface.
3. Results and discussion
3.1 Broadband absorption
The average absorption remains higher than 90% for the entire visible and near-infrared ranges, where solar spectrum has significant energy, as can be seen from AM 1.5 spectrum (Fig. 2(a)). The absorption decreases at longer wavelengths and becomes half of its maximum value at λ > 2500 nm, which is a desirable attribute for STPV systems in order to diminish thermal radiation. To enhance the thermal stability further and to protect the structure against oxidation, 15-nm thick coatings of HfO2, Si3N4, TiO2 and Cr2O3 are also proposed on top of the square ring design. The average absorption for 280 nm < λ < 2200 nm is 86% for uncoated absorber, whereas it is 88.96%, 84.25%, 90.67%, and 87.17% for HfO2, Si3N4, TiO2, and Cr2O3 coatings, respectively, as can be observed from Fig. 2(b).
Fig. 2. (a) Incident solar spectrum (AM 1.5) with spectral absorption of ideal absorber and simulated ZrN metasurface solar absorber. (b) absorption with and without coatings for HfO2, Si3N4, TiO2 and Cr2O3 layers of 15 nm.
3.2 Impedance matching
A metamaterial perfect absorber with a periodic nanostructure can be characterized through a homogeneous material described completely by its optical properties i.e. relative permittivity$\varepsilon (f) = {\varepsilon _0}{\varepsilon _r}$and permeability$\mu (f) = {\mu _0}{\mu _r}$, which, in combination, represent refractive index $n(f) = \sqrt {\varepsilon (f)\mu (f)}$and normalized impedance$z(f) = \sqrt {{{\mu (f)} / {\varepsilon (f)}}}$ [36]. For electromagnetic resonance occurring at a certain frequency, the impedance of designed structure matches that of free space i.e. z = 1, the reflectance diminishes, causing light energy confinement within the structure while transmittance in this case is already zero. The retrieved S-parameters from the proposed design are shown in Fig. 3(a-b), with ‘ε’, and ‘μ’ shown in Fig. 3(c-d). From these parameters, the refractive index ‘n’ and normalized impedance ‘z’ are given in Fig. 3(e-f), respectively. It can be observed from Fig. 3(f) that at λr = 630 nm, $z = 1.076 - 0.000012i\Omega $, which depicts that our proposed design is impedance-matched to the free space. In principle, the impedance at resonance depends on dimensions of the structure and the physical properties of the material. The impedance in terms of S-parameters of the structure is given by Eq. (1) [37]:
Fig. 3. (a) Magnitude and (b) phase of simulated S-parameters; real and imaginary parts of retrieved (c) permittivity (ε); (d) permeability (μ); (e) refractive index (n) and (f) impedance (z) from CST-MWS
Equation (2) is derived from Eq. (1), using mathematical simplifications and separating A into its real and imaginary parts. It can be seen that for A ∼ 1, the real part of z ∼ 1 and the imaginary part ∼ 0. From Fig. 3(f), it is clearly seen that normalized impedance lies close to 1 for the wavelengths where the absorption is high.
3.3 Polarization- and incidence angle-independence
The broadband absorption achieved by the proposed design is independent of the angle of incidence, as can be seen in Fig. 4(a) and Fig. 4(b) for TE (transverse electric) and TM (transverse magnetic) incident lights, respectively. Even for large oblique incident angles, strong average absorption is observed such that A = 92% at 60° for TM polarization and 87% for TE polarization in the visible regime. This shows that the magnetic field orientation is maintained so that the strength of magnetic resonance is kept the same at all incident angles. The designed structure is symmetric, and therefore, shows absorptance that is independent of polarization angle as well, as is depicted in Fig. 4(c), where polarization angles are varied from $\phi = 0^\circ $(TE-pol) to $\phi = 90^\circ $(TM-pol), showing insensitivity of the structure. Polarization-insensitivity is another necessary design requirement that stipulates maximum absorption for variable polarization and un-polarized sunlight [22]. Such characteristics lead to high efficiency for STPV systems when operated under high solar concentrations [38].
Fig. 4. (a) Absorption as a function of angle of incidence (${\theta } = 0^\circ \;\textrm{ to }\;60^\circ $) and wavelength; inset validating the independence of absorption w.r.t. ${{\theta }_\textrm{i}}$ for TE. (b) absorption as a function of angle of incidence (${\theta } = 0^\circ \;\textrm{ to }\;60^\circ $) and wavelength; inset validating the independence of absorption w.r.t. ${{\theta }_\textrm{i}}$ for TM. (c) absorption as a function of polarization angles (${\varphi } = 0^\circ \;\textrm{ to }\;90^\circ $ from TE polarization (0°) to TM polarization (90°) and wavelength; inset validating the independence of absorption w.r.t. ${\varphi _i}$. Simulated absorption of RMA with different structural parameters (d) height of the ring (e) width of the ring (f) height of the spacer, (g) height of the ground plane, and (h) calculated absorption for decoupled absorber based on interference model in comparison with the simulated absorption for coupled metamaterial absorber. Inset: Multiple reflections and interference model of the metamaterial absorber
3.4 Absorption spectrum and geometric parameters
In this section, we describe the relationship of geometrical parameters of nanostructure with absorption. Figure 4(d-g) show the absorption values for RMA when ‘hr’, ‘w’, ‘hs’ and ‘hg’ are varied over different ranges as hr = 20-60 nm, w = 30-70 nm, hs = 20-100 nm, and hg = 110-190 nm.
3.5 Multiple reflections interference model
In general, the MIM metamaterial absorber is taken as a coupled system, essentially the electric and magnetic resonances from two layers of metal take place, and hence free space matching is observed, which minimizes reflection. Additionally, the ground plane material being highly lossy causes zero transmission, leading to having high absorption.
However, in the light of interference model, the near-field interactions or magnetic response between the neighboring metals in a metamaterial absorber are not very significant, and they are linked just due to multiple reflections taking place between them. For a decoupled system, the unit-cell is considered to have two tuned interfaces, with ring-resonator and ground plane lying at two sides of the spacer. The light incident at the air-spacer interface is reflected back to the air and partially transmitted into the spacer, with a reflection coefficient ${\tilde{r}_{as}} = {r_{as}}{e^{j{\theta _{as}}}}$ and transmission coefficient${\tilde{t}_{as}} = {t_{as}}{e^{j{\theta _{as}}}}$, which transmits further, striking the ground plane with propagation phase$\beta = {n_{spacer}}{k_o}d$, where k0 is free space wavenumber. Again, it reflects back and at the air-spacer interface, with the coefficients ${\tilde{r}_{sa}} = {r_{sa}}{e^{j{\theta _{sa}}}}$ and${\tilde{t}_{sa}} = {t_{sa}}{e^{j{\theta _{sa}}}}$. The superposition of multiple reflections results in overall reflection given by:
3.6 Field intensity distributions
To further understand the physical mechanism behind ultra-broadband absorption, the electric (Fig. 5(a-c)), magnetic (Fig. 5(d-f)) field intensity distributions, the power flows, and the power loss densities are also investigated [14]. Electromagnetic field distribution is gathered for normal incidence along z-axis for 400, 630 and 800 nm and is shown for x-z plane. The electric field is localized within the ring cavity, while the magnetic field is localized within the spacer layer, along x-axis. The resonant electric field distribution occurs at reflection dip. As can be seen from Fig. 5 that at λr = 630 nm, the localized electric field is mainly concentrated within the ring structure, while the magnetic field is high at the outer edges. Moreover, from the profiles of power loss in Fig. 5(g-i), it is observed that the power loss is mainly concentrated in ZrN nanostructure, which is also consistent with the distributions of EM field.
Fig. 5. (a)-(c) Normalized electric field distribution profiles at λ = 400, 630 & 800 nm in x-z plane; (d)-(f) normalized magnetic field distribution profiles at λ = 400, 630 & 800 nm in x-z plane; (g)-(i) normalized power loss at λ = 400, 630 & 800 nm in x-z plane, respectively.
4. Emitter design
According to Kirchhoff’s law of thermal radiation, absorption is equal to emission at thermal equilibrium [40], which further means that a selective absorber will be a selective emitter at a certain operating temperature. A design comprising absorber and emitter, placed between the incident solar radiations and a PV cell, converts the broadband solar spectral radiation to selective narrowband radiation that is spectrally matched to the bandgap of PV cell. A PV cell with a high bandgap cannot fully absorb the solar spectrum, and if the bandgap is low, then most of the energy in high-energy photons is wasted. As reported in [41], III-V multi-junction (MJ) PV cells have an energy bandgap (Eg) ranging from 0.7 eV-1.9 eV for better conversion efficiencies. Figure 6 and Table 1 show that for the proposed emitter structure, the obtained BGs with different parameter sets lie in the range compatible with cell bandgap energies cited in [41], and that absorption for each of the designs is > 94.51%.
Fig. 6. (a) Emitter unit-cell with ground, spacer and ring for different Eg realizations. (b) variation of structural dimensions and obtained emittance in the range Eg = 0.5 eV to 3.0 eV. (c) angle-insensitivity of emitter design for S-polarization (d) angle-insensitivity of emitter design for P-polarization (e) retrieved impedance for emitter unit cell and (f) calculated emittance for decoupled structure based on interference model in comparison with the simulated emittance for coupled metamaterial absorber. Inset: multiple interference and interference model
Table 1. Design Parameters Variation for Realization of Different Bandgap Energies (eV)
In Fig. 6(a), the unit-cell for emitter design with variation of structural dimensions is presented for realization of different values of bandgap energies in the range where most of the PV cells are designed (0.7 eV to 1.9 eV), so that the selective emitter’s and solar cell’s Eg match. In Table 1 and Fig. 6(b), the obtained eV values with emittance/ absorbance are shown with respective changes in the structure, showing that the lowest observed value of emittance is 94.5% for 0.8 eV. The simple ring structure thus achieves excellent bandgap matching with the PV cells. In Fig. 6(c-d), the angle-insensitivity of the emitter design for both polarizations is shown. The proposed emitter design is also analyzed for impedance matching and the results are shown in Fig. 6(e). Finally, the application of interference theory is demonstrated through a comparison between simulated and calculated emittances for the proposed emitter design, covering bandgap energies between 0.5 eV – 3.0 eV (Fig. 6(f)).
5. Conclusion
In conclusion, a refractory metal nitride, ZrN-based absorber, is presented with the desired spectral response for STPV applications. The absorption of metamaterial structure is geometry-dependent, which is tuned to present maximum absorptance values of 99.70% and 99.54%, with and without coating, respectively, with an average absorptance of 95% for 400-800 nm, and 86.00% for 280-2200 nm. The average broadband absorptance is 88.96% for HfO2, 84.25% for Si3N4, 90.67% for TiO2, and 87.17% for Cr2O3 dielectric coatings with a thickness of 15 nm on top of the ZrN ring. The simple metasurface solar absorber exhibits high absorption for the frequencies where the solar spectral intensity is highly concentrated, while the emittance is highly suppressed at these frequencies to reduce thermal radiative loss. The metasurface thermal emitter allows for wavelength-selective emission that matches the bandgap of solar cells and the spectral peak of blackbody radiation to maximize thermal energy harvesting. The structure is highly resistive to environmental conditions and temperature degradation due to the high melting point of ZrN, which is 2980 °C. Multiple reflections and interference model.
The absorber is insensitive to change in incidence angle and polarization making it useful for complex electromagnetic conditions. It was observed that the electromagnetic resonances and dielectric loss of the structure have made such a high absorption possible. Moreover, analytically obtained results from interference theory are comparable to those obtained for a coupled system using simulations, which validates the results obtained through the simulation setup. In addition to STPV application, the thermal and chemical stability of composite materials makes them useful for high-power optoelectronics applications.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper may be obtained from authors upon request.
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