Abstract
In this paper, we propose an absorber with adjustable single-layer graphene multi-band perfect absorption, which has the advantages of simple structure, polarization insensitivity, tunability, multi-band absorption, and high sensitivity. The device can achieve four perfect absorption peaks at the same time, and the absorption rate of all absorption peaks is above 99%. The absorption effect of the absorber can be efficiently adjusted and controlled by adjusting the geometric parameters of the single-layer graphene array and the thickness of the dielectric layer. In addition, by changing the strength of the applied magnetic field, the Fermi level, and the relaxation rate of graphene, the absorption of the device can be dynamically adjusted, and high absorption can be maintained in the range of 0°–70° wide incidence angle. Finally, considering the potential sensing applications of the device, we measured maximum sensitivity (S) of 3.06 THz/RIU and a maximum figure of merit (FOM) of 54.6 when exposed to different ambient refractive indices, suggesting that the device can be used as a refractive index sensor. These results show that this study provides a new idea for the design of the tunable multi-band perfect metamaterial absorber based on graphene, which has great application value in many fields and provides a new reference for future research.
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Introduction
Metamaterials are a recently emerging type of artificial electromagnetic materials.1,2,3 Because of their unique sub-wavelength structure, they exhibit many unnatural phenomena, such as negative refractive index,4,5,6 perfect absorption,7,8,9 and electromagnetic transparency.10,11 At present, related metamaterial devices such as optical switches,12 modulators, and filters13,14,15,16 have been developed and widely used in the fields of terahertz (THz), infrared, and visible bands, providing many possibilities for light control. Metamaterial absorbers (MAs) are one of the most important applications of metamaterials. Because of their simple structure, convenient design, and extremely thin thickness, they have greater application prospects than traditional absorbers. In 2008, Landy et al.17 designed the structure of an MA which could produce effective electromagnetic resonance with incident electromagnetic waves in the THz radiation frequency range, and could achieve nearly 100% perfect absorption in a specific frequency range. However, given that metamaterial devices are designed to obtain ideal absorption effects, they will be designed with a unique structure.18,19,20 Once the device is manufactured, the structural parameters are difficult to change, so the spectral effect and effect are fixed. Therefore, MAs with greater flexibility and tunability have broader application prospects. Thus, we need to add some special materials that can control their electromagnetic properties by stimulating external factors.
Since Novoselov and Geim21 first prepared single-layer two-dimensional graphene flakes in 2004, researchers have found that graphene can replace traditional metal materials because of its excellent properties such as surface conductivity22 and high carrier mobility.23 This allows it to be used as a good platform for metamaterials and surface plasmons, which can exhibit strong constraints, unlike traditional surface plasmas such as gold and copper.24 In addition, the dynamic adjustability of graphene is an advantage for designing MAs.25 The surface conductivity of graphene is determined by the Fermi level, so we can adjust the Fermi level by applying a gate voltage and regulating the magnetic field and photoexcitation, and indirectly control the conductivity and permittivity of graphene.26,27 Consequently, graphene shines in the design of microwave metamaterials at THz bands and is widely used. For example, in 2019, Luo et al. proposed a dual-band polarization-insensitive perfect absorber that was tunable in the mid-infrared band, and obtained polarization-insensitive dual-band ideal absorption peaks at 9611 nm and 9924 nm, respectively.28 In 2021, Yin et al.29 proposed a three-dimensional dual-band perfect absorber that achieves absorption efficiencies of 99% and 97% at 1.125 THz and 1.1626 THz, respectively. In 2022, Chen et al.18 proposed a multi-band MA based on dart-type single-layer graphene, which has the advantages of multi-band, polarization independence, and tunability. Many studies30,31,32,33 have achieved good results, but these studies only focus on single-band or double-narrowband MAs, while multi-band absorbers are relatively rare, and the structure of current multi-band MAs is relatively complex due to stringent restrictions.
In this paper, we propose a multi-band perfect absorber based on single-layer graphene, which achieves multi-band perfect absorption at fI = 6.46 THz, fII = 7.49 THz, \(f_{{{\text{III}}}} { = 8}{\text{.53}}\) THz, and \(f_{{{\text{IV}}}} { = 9}{\text{.45}}\) THz with absorption rates of 99.68%, 99.60%, 99.87%, and 99.00%. Through the equivalent circuit model (ECM) and electric field distribution, the physical mechanism of perfect absorption is discussed. We then achieved dynamic tunability of the peak absorption spectrum and resonance frequency by adjusting the strength of the applied magnetic field, the Fermi level, and the relaxation rate of graphene. In addition, the influence of the geometric parameters of graphene and the structural parameters of the absorption band absorber is investigated. Finally, due to the symmetry of the geometry, we also explored that the absorber still has excellent absorption performance in a wide range of incidence angles. Finally, we investigated its sensing performance, with a maximum S and FOM of 3.06 THz/RIU and 54.6. In summary, the proposed structure has many potential advantages based on achieving perfect absorption in multiple bands. Compared with Liu et al.34, the proposed structure can generate more absorption peaks, with four absorption peaks greater than 99% at the same time. Compared with Zamzam et al.35, our proposed structure can maintain excellent absorption over a wider range of angle of incidence; even when the angle of incident light is 60°, the absorber can achieve an absorption rate of more than 90%. Compared with Cai et al.,36 the proposed structure is simpler and easier to manufacture, and our proposed structure can adjust the absorptivity of multiple absorption peaks with absorptivity greater than 99%.
Design and Method
The monolayer graphene-based MA proposed in this paper consists of three layers, as shown in Fig. 1a. At the top is an array of graphene patterns, consisting of a hollow “X” pattern and four isosceles right triangles. The middle layer is a silicon dioxide (SiO2) dielectric layer, and the bottom layer is gold (Au), forming a “sandwich” structure. During the simulation, the incident wave propagates vertically downward to the structural surface of the absorber, forming a multimode surface plasmon resonance. The relative permittivity of SiO2 is 3.9, and the relative permittivity function of the gold layer is represented by the Drude model37,38:
In this equation, \(\omega\) is the angular frequency of the incident light, \(\omega_{p} = 1.37 \times 10^{6}\) rad/s is the plasma oscillation frequency, and the electron collision frequency \(\gamma = 1.21 \times 10^{14}\) rad/s. Figure 1b shows a side view of the structure, showing the thickness of each layer of the absorber. The SiO2 layer thickness is h1 = 4.0 \(\mu {\text{m}}\). The thickness of the Au layer is h2 = 0.5 \(\mu {\text{m}}\), and the structure period P = 4 \(\mu {\text{m}}\). Figure 1c is a top view of a periodic monolayer graphene array, showing the detailed parameters of the pattern. The width of the “X” pattern is x1 = 0.3 \(\mu {\text{m}}\), and the length of one side is x2 = 2.4 \(\mu {\text{m}}\). The length of the base side of the isosceles right triangle is x3 = 2.4 \(\mu {\text{m}}\). The distance between the triangle and the center of the X pattern is d = 0.6 \(\mu {\text{m}}\).
We used the finite element method (COMSOL) for the simulation, set the period boundary conditions on the x- and y-axes, set the perfectly matched layers along the z-axis, and selected the appropriate mesh size to obtain excellent convergence results. So we can reflect the parameter \(S_{11}\) and transmit parameter \(S_{21}\). Since the thickness of the Au layer is much greater than its skin depth, the incident wave is almost completely reflected, which results in a transmittance \(T = \left| {S_{21} } \right|^{2} \approx 0\). Therefore, the absorption rate can be expressed as39
Furthermore, the appropriate size of the grid has been selected for excellent convergence. Since graphene has a gap-free electronic band structure and single atomic thickness, it can be used as a two-dimensional material to improve computational efficiency, and the surface conductivity is generally characterized by the Kubo formula32:
In the formula, \(e\) is the electron charge, \(k_{{\text{B}}}\) is the Boltzmann constant, \(T = 300\) K is the ambient temperature, \(\hbar\) is the Planck constant, \(\omega\) is the angular frequency of the incident wave, and \(E_{{\text{f}}}\) and \(\tau\) are the Fermi level and relaxation rate, respectively. Depending on the modulation structural parameters, it is found that the absorption effect is best when \(E_{{\text{f}}} = 1.0\) eV and \(\tau = 0.9\) ps. It is worth noting here that \(k_{{\text{B}}}\) is the Boltzmann constant, and in the infrared band according to the principle of Pauli incompatibility, because \(k_{{\text{B}}}\) is much smaller than \(E_{{\text{f}}}\) in the THz band, σinter can be ignored. So the conductivity formula of graphene can be expressed as40
According to the above equation, we can know that the conductivity of graphene depends on the Fermi level and relaxation rate, so we can achieve dynamic adjustment by adjusting the Fermi level and relaxation rate without changing the structural parameters of the absorbing device.
In practical experiments,41 a gold layer and a silica dielectric layer can be deposited on a silicon substrate by electron beam evaporation, and then a graphene layer can be grown on a copper catalyst by chemical vapor deposition. Then the “X” and isosceles triangle patterns were engraved by electron beam lithography and oxygen plasma etching to prepare a perfect absorber of single-layer graphene.
Results and Discussion
Figure 2 shows the absorption spectrum of a graphene-based multi-band MA designed by us. As a result, the absorber achieves multi-band perfect absorption at \(f_{{\text{I}}} { = 6}{\text{.46}}\) THz, \(f_{{{\text{II}}}} { = 7}{\text{.49}}\) THz, \(f_{{{\text{III}}}} { = 8}{\text{.53}}\) THz, and \(f_{{{\text{IV}}}} { = 9}{\text{.45}}\) THz, and the absorption rate reaches 99.68%, 99.60%, 99.87%, and 99.00%, corresponding to mode I, mode II, mode III, and mode IV. When the electromagnetic wave is incident perpendicular to the structure, the graphene on the surface is excited to produce a surface plasma, and the incident electromagnetic wave is consistent with the free electron frequency on the surface of the graphene, resulting in the phenomenon of surface plasmon resonance.42 The incident electromagnetic wave energy is used to excite plasma oscillations, and the energy is strongly absorbed, thus achieving perfect absorption.
As shown in Fig. 3, the operation mechanism of the device can be illustrated using ECM. The graphene pattern on the surface is represented by three RLC circuits connected in series, which are arranged in parallel in the circuit. One represents the cross pattern, and the other two represent the remaining four triangles. Resistors R1, R2, and R3 are related to the loss of the structure, with L1, L2, and L3 representing the inductance of the graphene pattern, and C1, C2, and C3 representing the electrical coupling between the graphene pattern and the metal ground.43
The reflection coefficient of a device can be expressed as
where \(Z_{{{\text{in}}}}\) and \(Z_{0}\) refer to the input impedance of MA and the intrinsic impedance of free space, respectively. In an equivalent circuit, \(Z_{{{\text{in}}}}\) can be written as
\(Z_{p1}\), \(Z_{p2}\), and \(Z_{p3}\) represent the impedances of the three parallel RLC circuits, and \(Z_{{{\text{in}}1}}\) represents the impedance of the short-circuit transmission line. The values of these impedances can be interpreted in this way:
where \(Z_{{\text{d}}} = Z_{0} /\sqrt {\varepsilon_{{\text{d}}} }\) is the characteristic impedance of the dielectric substrate and \(c\) is the speed of light. In addition, using quasi-static analysis, the equivalent inductance \(L_{j}\) and the equivalent capacitance \(C_{j}\) correspond to the length of the metal strip and the gap between adjacent cells, respectively.
In order to further reveal the physical mechanism of perfect absorption by absorbers, we studied the electric field distribution at the frequency of incident light \(f_{{\text{I}}} { = 6}{\text{.46}}\) THz, \(f_{{{\text{II}}}} { = 7}{\text{.49}}\) THz, \(f_{{{\text{III}}}} { = 8}{\text{.53}}\) THz, and \(f_{{{\text{IV}}}} { = 9}{\text{.45}}\) THz. Figure 4a, b, c, and d shows top views of the electric field distribution near graphene. The electric field at \(f_{{\text{I}}}\) is concentrated at the two vertices at the bottom of the upper and lower triangles, and \(f_{{{\text{II}}}}\) is the result of almost all triangle vertices acting together. The electric field strength at \(f_{{{\text{III}}}}\) is limited to the top of the bottom edges of the left and right triangles, and the electric field at the top of the bottom edges of the upper and lower triangles makes a small impurity peak in the absorption peak of \(f_{{{\text{III}}}}\). The resonance peak of \(f_{{{\text{IV}}}}\) is the result of the electric field at all the vertices of the upper and lower triangles. The four absorption peaks are mainly caused by the coupling between the vibration frequency of the graphene layer and the wavelength of the incident light, and the electric dipole resonance between the triangular pattern and the “X” pattern consumes the energy of the incident light, thus achieving perfect absorption.
In the actual work process, the incident wave is not only vertical, and the absorber must perform well under the condition of oblique incidence. Therefore, we studied the absorption of the absorber at a wide range of incident angles in the simulation process. First, we tested the absorption of MA at different polarization angles at perpendicular incidence, and as can be seen in Fig. 5, the absorption curves of MA are in perfect agreement with each other in the range of 0°–80° polarization. This indicates that the polarization angle has no effect on the absorption of the device, because the structure of the MA is highly symmetrical. As shown in Fig. 6a, the incident angle θ of the light source under the transverse electric (TE) mode polarization condition in the range of 0°–70°, the resonance wavelength is almost unchanged. As shown in Fig. 6b, under the transverse magnetic (TM) mode polarization condition, the absorber will hardly change with the increase of the incident angle, and when the incident angle at θ > 50°, the four absorption peaks have a slight blueshift. This is because, under the TM polarization condition, the dielectric constant of the waveguide layer of the absorber decreases with the increase of the incident angle. In addition, under the polarization conditions of TE and TM, the absorption of the absorber can achieve more than 99% absorption effect at the incidence angle θ ≤ 50°, and even when the incidence angle θ is 60°, the absorption effect of the four absorption peaks can achieve 90% and 94%. This proves that the multi-band perfect absorber of the single-layer graphene designed by us is not sensitive to angle, and in practical applications, we can design a matrix with a certain inclination angle so that the absorber attaches to its surface to increase the absorption effect, which provides more possibilities for the device.
The absorption effect of the absorber can be adjusted by changing the graphene pattern and structural parameters, but once the structure is fixed, it is difficult for us to change these parameters. However, due to the dynamic adjustability of graphene, we can flexibly manipulate absorption by adjusting the Fermi level and relaxation rate of graphene. Figure 7 shows the effect of the Fermi level on multi-band absorption performance. It can be seen from the figure that when the Fermi level increases from 0.7 eV to 1.0 eV, the absorption intensity increases continuously and a significant blue shift occurs. This phenomenon can be explained by resonance conditions.44,45 The formula is as follows:
where \(\lambda_{\gamma }\) is the resonant wavelength, \(L\) is the graphene nanoribbon length, and \(\alpha_{0} = e^{2} /(\hbar c)\) is the coefficient related to the geometry of the model. It can be seen from this equation that with the increase of \(E_{F}\), the resonance wavelength \(\lambda_{\gamma }\) decreases, and the blue shift phenomenon occurs. This also shows that when the geometric parameters of the absorber are fixed, we can adjust the absorption of the absorber by changing the Fermi level.
Next is the effect of relaxation rate on multi-band absorption performance. As can be seen from Fig. 8, as the relaxation rate increases from 0.5 ps to 0.9 ps, the peak value of the absorption peak of \(f_{{{\text{III}}}}\) increases, and the peak of the absorption peak at the other three resonant frequencies increases. The reason for this phenomenon is that the increase in relaxation rate will improve the effect of carriers on plasma oscillations, but at certain frequencies, if the relaxation rate is large enough, it will cause the carriers to be saturated, the energy will be reflected, and the peak of the absorption will be reduced.46,47
Considering that the strength of the applied magnetic field also has an effect on the conductivity of graphene, we studied the absorption of MA under different applied magnetic field strengths. As shown in Fig. 9, it can be seen that as the magnetic field strength increases, the frequency corresponding to the absorption peak shifts to the high frequency, and a blue shift occurs. When we apply a magnetic field perpendicular to the surface of graphene, the conductivity of graphene becomes in the form of tensor, the expression of which is55,56:
Each component can be expressed as
\(\tau = 1/\Gamma\) in the formula is the relaxation time and \(\omega_{c} = eBV_{f}^{2} /E_{{\text{f}}}\) is the electron rotation frequency of graphene. From the above component formula, we can see that the conductivity component of graphene \(\sigma_{zz}\) is independent of the magnetic field, so when the applied magnetic field strength is zero, the conductivity tensor will become a matrix with equal diagonal elements and zero diagonal elements, that is, graphene is an isotropic medium at this time. When the applied magnetic field strength is non-zero, the conductivity becomes anisotropic, which can cause the plasmon on the surface of graphene to propagate in different directions. Therefore, we can control the dynamic control of the device by controlling the strength of the applied magnetic field.
We further investigate how structural parameters and the size of geometric patterns affect multi-band absorption. In this study, we consistently maintained a Fermi level and relaxation rate of 1.0 eV and 0.9 ps, respectively. First, we studied the relationship between the absorption performance of the absorber and the thickness of the dielectric layer, as shown in Fig. 10a. When the pattern parameters were fixed, the absorption peak underwent a significant redshift when the dielectric layer increased from 3.7 \(\mu {\text{m}}\) to 4.0 \(\mu {\text{m}}\), and the absorption peak-to-peak of fII gradually increased with the increase of the thickness of the dielectric layer, from 96.86% to 99.60%. This can be explained using the interference theory. Part of the incident wave is reflected directly by the graphene on the surface of the absorber, and the rest is transmitted to the dielectric layer, where it is reflected several times and then propagated to the top surface again. The dielectric layer plays an important role as a Fabry–Perot resonator during absorption,48,49 and its thickness leads to constructive/destructive interference and further modulates the absorption spectrum.
Next, we investigate the influence of the geometric parameters of the pattern on the performance of the absorber, as shown in Fig. 10b. Under the premise of fixing other parameters, when the length of the bottom edge of the triangle pattern changed from 2.2 \(\mu {\text{m}}\) to 2.5 \(\mu {\text{m}}\), fI and fIII remained relatively stable, fII underwent obvious redshift, and fIV showed first a blue shift and then a red shift. This is because when the distance between the triangle and the X figure is close, fI and fII, fIII, and fIV interact, and once the distance reaches the critical limit, the original resonant mode is destroyed and a new resonant mode is excited.50
Finally, we investigated the sensing performance of MA in detecting changes in the refractive index of some specific analytes. We replace the air medium covered with the MA with the analyte to be detected. The refractive index of these substances ranges from 1.33 to 1.5, which includes water (refractive index 1.33), ethanol (refractive index 1.36), ethylene glycol (refractive index 1.41), cyclohexane (refractive index 1.45), and benzene (refractive index 1.5). As shown in Fig. 11a, at room temperature, as the refractive index of the different analytes increases, the four absorption peaks are significantly redshifted. Except for a slight decrease in the fII absorption peak, the absorption efficiency of the absorption peaks remained almost unchanged. This indicates that analytes with different refractive indices can be resolved by shifting the resonant frequency of the absorption peak due to a change in the refractive index. To further investigate the sensor performance of MA, sensitivity (S) and the figure of merit (FOM) are two parameters commonly used to evaluate device performance. Defined as51,52,53
\(S\) represents the frequency shift of the refractive index unit (RIU) change. \(\frac{\Delta A}{{\Delta n}}\) represents the change in relative peak absorptivity caused by the change in refractive index \(\Delta n\).
As shown in Fig. 11b, the sensitivities of the four absorption peaks are SI = 2.35 THz/RIU, SII = 2.58 THz/RIU, SIII = 2.71 THz/RIU, and \(S_{{{\text{IV}}}} { = 3}{\text{.06}}\) THz/RIU, respectively. In addition, the calculation shows that the maximum FOM value can reach 54.6.
Finally, we compared the proposed MA with some of the reported devices, as shown in Table I. The results show that the device we designed not only has multiple absorption bands, but also has better sensing performance. This provides a more valuable reference for further design and research of graphene-based MAs.
Conclusion
In summary, this paper describes the design and study of a multi-band perfect absorber based on a single layer of graphene, which is composed of a single-layer patterned graphene, a silica dielectric layer, and a gold substrate, which has the characteristics of simple structure. Using the COMSOL commercial software, it is confirmed that the absorber has absorption peaks of 99.99%, 99.60%, 99.87%, and 99.00% at fI = 6.46 THz, fII = 7.49 THz, fIII = 8.53 THz, and \(f_{{{\text{IV}}}} { = 9}{\text{.45}}\) THz, respectively, and can maintain absorption of more than 90% at a wide range of incidence angles of 0°–70°. At the same time, we proved the multi-band perfect absorption principle of the device through the ECM and internal electric field analysis. In addition, the optical properties of the absorption spectrum are further revealed by changing the thickness of the dielectric layer and changing the size of the graphene pattern. In addition, by adjusting the strength of the applied magnetic field, the Fermi level, and the relaxation rate of graphene, the resonance wavelength and absorption efficiency of the absorber can be dynamically adjusted. Finally, the sensing performance of the absorber was investigated by varying the analytes overlaid on the device, with the highest S and FOM of 3.06 THz/RIU and 54.6 for the absorber. Therefore, the device has broad application prospects in photoelectric sensing and chemical detection, and also provides an important reference value for the research in this field.
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Funding
This study was funded by the Open Research Fund of State Key Laboratory of Advanced Technology for Materials Synthesis and Processing (Wuhan University of Technology) (Grant Number: 2022-KF-15), the Open Research Fund of State Key Laboratory of Millimeter Waves (Grant Number: K201606), the National Natural Science Foundation of China (Grant Number: 11664025), and the Chongqing Natural Science Foundation (Grant Number: CSTB2023NSCQ-MSX0730).
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Song, Y., Deng, XH., Zhang, P. et al. Graphene-Based Metamaterial Absorber with Perfect Multi-band Absorption. J. Electron. Mater. 53, 4049–4058 (2024). https://doi.org/10.1007/s11664-024-11108-7
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DOI: https://doi.org/10.1007/s11664-024-11108-7