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Abstract
It is well known that both graphene and monolayer black phosphorus (BP) can excite and generate surface plasmonic resonances in the infrared spectrum, providing suitable conditions for strong light-matter interactions. To take full advantage of this benefit, a three-layered infrared absorbing structure with broadband absorption effect based on a hybrid graphene-BP metamaterial was developed. Using numerical research methods, the absorption effect of the structure could be well modulated by adjusting the geometrical parameters of the structure and the doping levels of graphene and BP. In addition, the sensitivity of the structure to the angle of incidence is also investigated. By optimizing the previous parameters, the structure achieves an absorption of more than 87.5% in the wavelength range from 10.1 to 24.5 um and a maximum absorption of 99.97%. The proposed broadband infrared structure could have many potential applications in infrared sensing, bio-imaging and environmental monitoring.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
It is well known that graphene and black phosphorus (BP) are two-dimensional materials with excellent optical and electrical properties, which have been intensively studied and have become a focus of scientific research [1]. Metamaterials are electromagnetic materials with an artificially designed periodic arrangement of sub-wavelength microstructures [2,3]. There are a variety of applications in structures that act as solar cells [4,5], invisibility cloaks [6], etc. Graphene is a honeycomb crystal structure of densely packed carbon atoms linked by sp2 hybridization [7], with in-plane anisotropic optical and electrical properties [8–11]. Graphene also has remarkable carrier mobility and is widely employed in nanophotonic devices such as photodetectors [12], sensors [13], and light absorbers [14], plasmon-induced transparency based devices [15], polarization beam splitters [16], modulaters [17] and so on. However, graphene has no band gap, which limits its use in structures with a high on-off ratio.
BP, on the other hand, compensates for the lack of band gap in graphene. BP is a ruffled hexagonal ring formed by the sp3 hybridization of phosphorus atoms [18]. BP exhibits a high degree of anisotropy due to the ruffled structure, as the effective masses of BP in the armchair (x-direction) and zigzag (y-direction) directions are formally equal [19–21]. The band gap of the BP is tunable and is affected by the thickness of the BP [18]. BP also has properties such as strong interactions with light in the mid-infrared region, high carrier mobility and carrier density [22]. Due to these excellent optoelectronic properties, BP is widely used in photodetectors [23], heterojunction p-n diodes [24], saturable absorbers [25], and so on. However, the plasmon resonance of the structure using black phosphorus alone is relatively weak, which limits its anisotropic nature. Therefore, a broadband infrared absorber based on a mixture of graphene and BP was developed, combining the advantages of both materials.
Cai et al. proposed an anisotropic infrared plasma broadband absorber based on a graphene-BP multilayer film, a mixture of graphene and black phosphorus used to form a three-layer sandwich structure. The structure combines the respective advantages of graphene and black phosphorus and can achieve highly anisotropic broadband absorption [26]. Xiao et al. investigated tunable and anisotropic perfect absorbers in graphene-black phosphorus nanoblock array structures by numerical analysis. The structure exhibits polarization-dependent anisotropic absorption in the mid-infrared, while the absorption spectrum of the structure can be tailored using geometric parameters, graphene and BP doping, which has the potential for developing polarization-selective and tunable high-performance mid-infrared devices [27]. Nong et al. have theoretically investigated the hybridization of graphene surface equipartition excitations (GSP) and anisotropic black phosphorus localized surface plasmas (BPLSP) in a strongly coupled state. The paper enables strongly coherent GSP-BPLSP coupling in both armchair and sawtooth directions [28]. Li et al. proposed a wide-angle and tunable perfect absorber in the mid-infrared band based on the critical coupling of graphene and BP in the mid-infrared band. The structure couples iso-excitations of graphene and black phosphorus and utilizes the critical coupling while controlling the position of the perfect absorption peak by tuning the Fermi energy level of the material [29]. The above-mentioned absorbers have the disadvantages of narrow broadband absorption and not high enough absorption rate, or require relatively complex preparation techniques.
In this article, the advantages of BP and graphene are combined to design a near-uniform broadband infrared absorber with a graphene black phosphorus bimodal triple-layer structure using a mixture of both materials. The structural parameters as well as the chemical parameters of this absorber are analyzed and optimized. The results of the absorber show that its broadband absorption is stronger than that of any single material, with a maximum absorption close to one unit.
2. Materials and methods
Figure 1 shows that a base unit of a constructed absorber contains a three-layer graphene-BP bimodal structure. In the structure, an insulating layer of silicon dioxide (SiO2) is used to separate the single layer of graphene from the single layer of BP. This is used to block charge carrier transport between the graphene and monolayer BP to ensure their high charge carrier mobility. The first layer of the structure consists of a rectangle with lengths and widths a1 and b1, respectively; the second layer consists of two identical rectangles with lengths and widths a2 and b2, respectively, stacked symmetrically; the third layer, similar to the first, is a rectangle with lengths and widths a3 and b3, respectively. The unit cycle length is p, the thickness of the dielectric layer is d1, the thickness of the insulating layer is d2, and each layer has a spacing of d3. The three-layer structure formed by the simultaneous combination is wrapped in aluminium oxide (Al2O3) and deposited on an Al2O3 substrate. The dielectric constants of SiO2 and Al2O3 used are 3.9 and 3.2 respectively.
Fig. 1. Schematic diagram of a graphene-black phosphorus bimodal triple-layer structure for broadband infrared absorbers. (a) Perspective view. (b) Cross-section view. (c) Top view.
The finite element method (FEM) is applied to simulate and study the broadband absorption properties of a graphene-BP bimodal triple-layer structure of a broadband infrared absorber. In the FEM simulation, we employ the periodic Floquet conditions in x and y directions. A triangular mesh is used for the graphene layer, the monolayer BP, and the periodic boundary conditions. The triangular mesh partitioning is refined for the graphene layer and the single layer BP, and a tetrahedral mesh is used for the rest of the structure. The incident light is directed downward from the top of the structure with the direction perpendicular to the top, and the boundary conditions at the bottom are set to PEC boundary conditions. The incident light is s-polarized light. The PEC is an ideal boundary condition, a lossless surface; it has a reflectance of 1. Since the PEC boundary condition is used, the transmission rate is zero and the transmission ratio T=|S21|2 is zero. The absorbance of the absorber, A = 1-T-R, can then be simplified to A = 1-R. Here, R=|S11|2, and S11 stands for the scattering coefficient of the reflection loss, which can be obtained directly from the FEM simulation. Since the thicknesses of the graphene and BP layers are too small, we assume that they have a thickness of zero in the simulation and use the surface conductivity to calculate the corresponding electric field component. This improves the computational efficiency while ensuring the accuracy of the calculation.
The surface conductivity of graphene is modelled by the Kubo equation as [30]
The surface conductivity equation for a single layer of BP using the semi-classical Drude model is given by [31]
Here, σx, σy denote the surface conductivity in the x and y directions, and Dx, Dy denote the Drude weight in the x and y directions, depending on the effective electron mass mj in the x or y direction. η denotes the relaxation rate, which determines the relaxation rate of BP, and is set to 10 meV for the simulation. ns represents the doping level of the electrons and is set to 2 × 1013 cm-2 for the simulation. The electron mass in the x or y direction can be calculated by the following equation:
where3. Simulation results
Before analyzing the three-layer structure of graphene-BP, we simulated the second layer of the “+” structure with two identical rectangles of length and width a2 and b2, respectively, stacked symmetrically, and the single-layer model of the “+” structure is shown in Fig. 2.
Fig. 2. Single-layer decamer model of a graphene-BP hybrid, where the period is set to p, the thickness of the insulating layer is set to d2, the length and width of the two identical rectangles are set to a2 and b2 respectively, the thickness of the dielectric layer is set to d1 and the layer spacing is set to d3. (a) Perspective view. (b) Top view. (c) Cross-sectional view.
First, to observe the effects of the three-layer structure on the absorption spectrum in detail, we analyze the effect of the thickness of the insulating layer on the absorption spectrum of the structure. As shown in Fig. 3(a), as the thickness of the insulating layer increases, the resonance band of the absorption spectrum increases and then decreases, as does the absorption effect. When d2 is in the range of 5∼40 nm, the resonance wavelength is red-shifted and the resonance band becomes wider. d2 is in the range of 41∼80 nm, the resonance band decreases and the absorption effect is weakened. d2 = 20∼50 nm, the absorption peak of λ=15 um is stable near unity. The mixture of graphene and black phosphorus produces a broad absorption effect [28]. Meanwhile, because the structure is a superposition of two identical rectangles, the number of resonance modes increases relative to a single rectangle, and multiple resonance absorption peaks are connected together to form a broadband absorption. Thus, in Fig. 3(b), a broadband absorption with the presence of three absorption peaks appears in the absorption spectrum of the structure when d2 = 22, 25 and 30 nm. When d2 = 22 nm, one absorption peak is 99.74%, corresponding to a wavelength of 12.2 um; the second absorption peak is 99.93%, corresponding to a wavelength of 15.6 um; and the third absorption peak is 94.90%, corresponding to a wavelength of 18.6 um. This is due to the small spacing between the graphene and BP layers and the rather strong near-field scattered by the graphene and BP nanoparticles compared to the incident excitation field, which leads to a strong coupling of the scattered fields of each graphene-BP nanoparticle. Moreover, the superposition of the inverse electromagnetic field caused by the electric dipole excited by the incident light helps to suppress the reflectivity. This results in a near-unit absorption effect as well. When d2 is increased to 25 and 30 nm, the three peaks decrease by less than 5%, corresponding to a wavelength shift of less than 0.5 um. Overall, the absorption effect decreases sharply between the first and second peaks and can reach a low level of 50.16%. The absorption between the second and third peaks also decreases, but the decrease is less than the first peak and can still be maintained at a minimum of 80.87%.
Fig. 3. Absorption spectra of single-layer “+” structures with fixed period p = 250 nm, graphene Fermi energy level μc1 = 0.7 eV, BP Fermi energy level μc2 = 0.6 eV, dielectric layer thickness d1 = 1.65 um, rectangular aspect a2 = 200 nm, b2 = 150 nm. (a) Absorption spectra of single-layer “+” structures for different insulating layer thicknesses d2 = 22, 25, 30 nm. (b) Absorption spectra of single-layer “+” structures for d2 = 22, 25, 30 nm. The layer spacing thickness d3 is 150 nm. (c) Absorption spectra of single-layer “+” structures corresponding to different values of layer spacer thickness d3. (d) Absorption spectra of the single-layer “+” structure for d3 = 105, 150 and 187 nm. The insulation thickness d2 is 25 nm.
Second, the effect of the layer spacing on the total absorption of the monolayer of the “+” structure is investigated. Figure 3(c) shows that the resonance wavelength corresponding to the first absorption peak appears red-shifted from 50 nm to 200 nm as the layer spacing d3 increases, gradually approaching that corresponding to the second and third absorption peaks without changing significantly. The increase of the layer spacing corresponds to a thickening of the Al2O3 around the graphene-BP structure and an increase of the effective refractive index around it, hence the red-shift of the resonance wavelength and the accompanying change of the absorption spectrum. As shown in Fig. 3(d), the peak and wavelength of the three absorption peaks do not change significantly when the layer spacing is increased from 105 nm to 187 nm, and the descent curve between the second and third absorption peaks also changes less. The increase in the absorption curve between the first and second absorption peaks is significant, with the minimum value increasing from 50.16% to 80.41%. The absorption spectrum was able to maintain the high absorption effect of the remaining two peaks while increasing the minimum absorption value. This is because when the layer spacing d3 increases, the absorption peaks of different resonance modes corresponding to the resonance wavelengths are shifted and the degree of superposition increases, which corresponds to an increase in the absorption rate of the troughs, resulting in a smoother curve of the absorption spectrum.
The absorption spectra can be seen in Fig. 4 as the electric field distribution in the x- and z-axis directions at λ = 12.1, 15.4, 18.5 and 19.0 um for a dielectric layer thickness of d2 = 25 nm. It can be seen that both graphene and BP contribute to the total absorption of the monolayer “+” structure. As can be seen from Figs. 4(a)-(d), the electric field is mainly concentrated at the sharp edges on the graphene side of the graphene-BP structure. Due to the strong plasma excitation by graphene, the incident field at the corresponding resonance wavelength excites the electrons in the graphene to oscillate in the direction of the electric field, resulting in the incident field being mainly concentrated on the surface of the graphene side. At the same time, the strong electric field induced by the excitation of the graphene plasma also leads to a concentration of the electric field on the BP side, as shown in Figs. 4(e)-(h).
Fig. 4. Electric field distribution of the three absorption peaks at insulation thickness d2 = 25 nm. (a) Electric field distribution in the z-axis direction at resonant wavelength λ=12.1 um. (b) Electric field distribution in the z-axis direction at resonant wavelength λ=15.4 um. (c) Electric field distribution in the z-axis direction at resonant wavelength λ=18.5 um. (d) Electric field distribution in the z-axis direction at resonant wavelength λ=19.0 um. (e) Electric field distribution in the x-axis direction at resonant wavelength λ=12.1 um. (f) Electric field distribution in the x-axis direction at resonant wavelength λ=15.4 um. (g) Electric field distribution in the x-axis direction at resonant wavelength λ=18.5 um. (h) Electric field distribution in the x-axis direction at a resonant wavelength λ = 19.0 um.
There is a clear diffusion and redshift of the resonance band as the rectangular length a2 increases from 160 nm to 230 nm in Fig. 5(a). The first absorption peak is too small and insignificant at a2 = 160 to 195 nm and increases significantly at a2 = 196 to 230 nm. The third absorption peak is too small and insignificant at a2 = 160∼185 nm and increases significantly at a2 = 186∼230 nm. When a2 increases to 196 nm, the excited plasmonic resonance is enhanced due to the increased material coverage of graphene and the monolayer BP, while the near-field effect of graphene and the monolayer BP is also enhanced, resulting in overlapping peaks and many zigzag lines in the absorption curve. In Fig. 5(b), the rectangular width b2 increases from 100 nm to 200 nm, with a redshift of the first and second resonance wavelengths and a gradual shift to the third resonance wavelength. Similar to the parameter a2, when b2 increases to 140 nm, the excited plasmonic resonance is enhanced due to the increased material coverage of graphene and the monolayer BP, together with the enhanced near-field effect of graphene and the monolayer BP, resulting in many ripples in the absorption curve.
Fig. 5. Fixed period p = 250 nm, graphene Fermi energy level μc1 = 0.7 eV, BP Fermi energy level μc2 = 0.6 eV, dielectric layer thickness d1 = 1.65 um, layer spacing d3 = 187 nm. (a) Absorption spectra of single-layer “+” structures for different values of length a2 structures. The rectangular width b2 is 150 nm. (b) Absorption spectra of monolayer “+” structures corresponding to different values of width b2. The rectangular length a2 is 200 nm.
Changes in the Fermi energy levels of graphene and the monolayer BP affect the absorption spectra in a similar way, as shown in Fig. 6(a). Let μc1 = 1.0 eV, μc2 = 0.8 eV be condition 1 and μc1 = 0.7 eV, μc2 = 0.6 eV be condition 2. The maximum absorption of the absorption spectra of the structures under both conditions can reach nearly one unit and the width of the resonance band can reach 6 um. In condition 2, a red shift can be seen with respect to the resonance band of condition 1, and the width of the resonance band is slightly broadened by 0.6 um, but the minimum absorption of condition 2 is only 80.84%, which is much lower than that of condition 1 with 88.85%, as shown in Table 1. As can be seen in Fig. 6(b), when the incidence angle θ is kept between 0 and 50°, the absorption rate in the range of 10-16 um remains above 80% when the incidence angle θ is increased to 59°, the absorption rate remains above 70%; only when the incidence angle θ is increased above 66° does the absorption rate of the structure fall below 60%. As for the final results, the single-layer “+” structure is less sensitive to the incident angle and the robustness of the structure is very good. The comparative analysis in Fig. 6(c) indicates that a single-layer “+” structure is superior to the two materials used individually in the case of a mixture of graphene and BP.
Fig. 6. Fixed period p = 250 nm, dielectric layer thickness d1 = 1.65 um, layer spacing d3 = 187 nm, rectangular aspect a2 = 200 nm, b2 = 150 nm. (a) Absorption spectra of structures with μc1 = 1.0 eV, μc2 = 0.8 eV and μc1 = 0.7 eV, μc2 = 0.6 eV. (b) Absorption spectra of the structure at different incidence angles for μc1 = 1.0 eV, μc2 = 0.8 eV. (c) Absorption spectra of structures using graphene-BP, graphene, and BP materials with the remaining parameters fixed.
Table 1. Absorption spectral data for structures when μc1 = 1.0 eV, μc2 = 0.8 eV, μc1 = 0.7 eV, μc2 = 0.6 eV, holding other parameters constant.
There are three main methods to achieve broadband absorption, one is planar design, which means that different structural units are arranged in orderly combinations in the same plane to achieve broadband absorption. The second method is longitudinal stacking, which uses a multilayer metal and dielectric layer longitudinal alternating stacking structure to achieve broadband absorption, and the third method is a combination of planar and longitudinal design. We use the longitudinal stacking method and combine it with the sandwich structure. Thus, after optimisation of the graphene-BP hybrid monolayer “+” structure, the number of layers was extended to three, i.e., a rectangular graphene-BP hybrid structure was added at the top and bottom of the “+” structure, which was united with Al2O3. The rectangular graphene-BP hybrid structure is encapsulated in Al2O3 and deposited on an Al2O3 layer. Figures 7(a)-(c) show the effect of the Fermi energy level of each layer on the absorption spectrum of the structure. It can be seen that the variation of the monolayer BP Fermi energy level μc12 in the first layer has a small effect on the absorption spectrum, with a small bifurcation in the absorption spectrum only when the value of μc12 exceeds 0.7 eV. Smaller Fermi energy levels μc22 and μc32 in the second and third layers of the monolayer BP lead to a strong attenuation of the absorption, accompanied by a narrowing of the absorption bandwidth. After optimizing the three-layer structure in the same way as the single-layer “+” structure, an absorption spectrum with an extended bandwidth of 14.4 um and a resonance band of 10.1 to 24.5 um was obtained, and the maximum absorption of 99.97% was still achieved while the minimum absorption was kept at 87.5%, as shown in Fig. 7(d).
Fig. 7. Absorption spectra of the graphene-BP hybrid using three layers of the structure, where the first rectangular length and width of the first layer a1 = 131 nm, b1 = 174 nm, and the third rectangular length and width of the third layer a3 = 221 nm, b3 = 156 nm, (a) absorption spectra of the structure for different values of μc12. (b) absorption spectra of the structure for different values of μc22. (c) absorption spectra of the structure for different values of μc32. (d) absorption spectra of the structure at μc12 = 0.5 eV, μc22 = 0.8 eV, μc32 = 0.7 eV with the remaining parameters fixed.
In Fig. 8, the incidence angle of the three-layer structure with graphene hybrid BP is analyzed, and it is found that when the incidence angle θ is 0∼40°, the absorption rate in the range of 10.1∼24.5 um is over 80%; when the incidence angle θ increases to 50°, the absorption rate remains over 70%; only when the incidence angle θ increases to over 67°, the absorption rate of the structure drops to below 60%. According to the final results, the three-layer graphene-BP hybrid structure has the same low sensitivity to the incident angle as the single-layer “+” structure, and the robustness of the structure is very good.
From the above simulation analysis, the single-layer graphene-BP hybrid structure can achieve a broadband absorption of more than 88.85% in the band from 10.0 to 16.0 um, and the maximum absorption rate can reach 99.95% by optimizing the geometric parameters and matching the Fermi energy levels of graphene and BP. When the incidence angle is within 50°, the absorption rate can be maintained above 80% with good structural robustness. Tuning optimization of the Fermi energy level of the graphene, and the monolayer BP results in a shift of the resonance wavelength. The shift occurs because the effective wavelength of the absorber is affected by the operating wavelength and the effective refractive index. At a fixed wavelength, an increase in the Fermi energy level or leads to a decrease in the effective refractive index, resulting in a blue shift of the resonant band. The three-layer structure increases the interaction between the graphene and the monolayer BP, resulting in multiple resonances and thus a broadening of the resonance band.
4. Discussions and conclusions
In this article, we mainly introduce a three-layer graphene-BP hybrid plasmonic nanostructure and numerically show that it has a broadband strong absorption effect that neither the single layer of graphene nor the BP has. To investigate the role of the individual layers, we first analyze the single-layer graphene-BP hybrid “+” structure and demonstrate that strong broadband absorption can be achieved under these conditions and that the structure is less sensitive to the angle of incidence. Moreover, for the rectangular graphene-BP hybrid structure with one layer above and one layer below the single-layer structure, it is shown that a significant broadening of the absorption bandwidth can be achieved and the absorption effect and sensitivity to the incident angle are not greatly reduced by the multilayer structure. Thanks to these excellent properties, the hybrid three-layer plasmonic nanostructures could have potential applications in infrared sensing, bioimaging and environmental monitoring.
Funding
Program for Excellent Scientific and Innovation Research Team (2022AH010002); Natural Science Foundation of Anhui Province (2022AH030014); National Natural Science Foundation of China (62101333, 62271001, U20A20164).
Disclosures
The authors declare no conflict of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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