A novel multilayer photonic structure is proposed to achieve the strong enhancement of light absorption in monolayer molybdenum disulfide (MoS2). Both numerical and analytical results illustrate that the absolute absorption of light in this atomically thin layer can approach as high as 96% at the visible wavelengths due to the excitation of Tamm plasmon mode. It is also found that the operating wavelength and height of sharp absorption peak are particularly dependent on the layer thicknesses and period number of dielectric grating, MoS2 position in the spacer, and incident angle of light, which contribute to the tunability and selectivity of light-MoS2 interaction. These results would provide a new pathway for the improvement of MoS2 photoluminescence and photodetection.
© 2017 Optical Society of America
Two-dimensional (2D) materials, such as graphene and transition metal dichalcogenides (TMDCs), have been regarded as a newly emerging platform for the development and revolution of photonic and optoelectronic devices due to their excellent mechanical, electric, and optical properties . Graphene with extremely high carrier mobility, broad spectral range, dynamic tunability, and compatibility with other photonic structures facilitates novel functional devices including fiber polarizers , photodetectors , mode-locking lasers , and slow light components . Unlike graphene, the TMDC materials possess unique band structures similar to semiconductors, which are beneficial to the optoelectronic applications. As a special TMDC semiconductor, molybdenum disulfide (MoS2) has attracted particular attention and found important applications in the photoluminescence, photodetection, and photovoltaic devices [6–8]. This is attributed to the appearance of direct bandgap (1.8 eV) for electronic transition when MoS2 multilayers are transformed to monolayer . This fascinating property of monolayer MoS2 gives rise to the ultra-high on/off ratio for field effect transistors . Even so, the atomically thin layer exhibits absolutely low absorption of light. For instance, the absorption of light in monolayer MoS2 on silica substrate is less than 8% in the visible range from 400 to 700 nm . The average single-pass absorption in monolayer MoS2 is about 10% in this spectral range . The intrinsically poor light absorption of monolayer MoS2 induces the weak light-matter interaction in MoS2 and thus, resists its substantial applications in optoelectronic devices . Enhancing light absorption of this 2D atomic layer plays a crucial role in enabling broad applications of MoS2 in optoelectronics [11, 12]. Recently, several schemes were proposed to improve the light absorption of MoS2 [11–17]. The chirped Bragg reflector was used to realize the visible light absorption of 33% in the monolayer MoS2 . The nanocavity with an aluminum reflector could increase the light absorption of monolayer MoS2 to nearly 70% at the wavelength of 450 nm . Piper et al. proposed the photonic crystal slab with a perfect conductor mirror to achieve near-unity absorption at 450 nm and average absorption of 51% over the spectrum from 400 to 700 nm in the MoS2 layer . The magnetic coupling metasurface could boost the light absorption of monolayer MoS2 to 72.7% . Particularly, the plasmonic resonances in metallic nanostructures were widely used to improve the light absorption of MoS2, providing a feasible avenue toward the selective enhancement of the photocurrent and photoluminescence in MoS2 [6, 15–17]. But, the improvement of light absorption of monolayer MoS2 is limited by the inherent loss of plasmonic resonances .
In this paper, we propose a new multilayer photonic configuration consisting of a dielectric Bragg grating, a metal film, and a spacer between them for the enhancement of light absorption of monolayer MoS2 inserted in the spacer. The finite-difference time-domain (FDTD) simulations show that the absorption of light in monolayer MoS2 can reach as high as 96% due to the strong field confinement of Tamm plasmon (TP) modes in the spacer, which is a remarkable value compared with the previous results. The simulation results agree well with the analytical calculations. Meanwhile, the operating wavelength and efficiency of MoS2 absorption strongly rely on the layer thicknesses and period number of dielectric grating, MoS2 position in the spacer, and incident angle of light. These results can offer a promising way for the tunability and selectivity of the enhancement of light-matter interaction in 2D materials, and find special applications in the MoS2 photoluminescence and photodetection.
2. Structure and model
As depicted in Fig. 1(a), the proposed configuration is composed of a dielectric Bragg grating, a metal film deposited on a substrate, a spacer between the grating and metal film. The monolayer MoS2 is inserted in the spacer. The light with angle θ is incident and propagates in the multilayer structure. Here, the alternatively stacked layers of Bragg grating are selected as Silicon dioxide (SiO2) and Titanium dioxide (TiO2), whose refractive indices can be set as ns = 1.45 and nt = 2.13 in the wavelengths of interest, respectively [18,19]. The complex permittivity of metal (silver) can be typically described by the Drude model: εAg(ω) = ε∞-ωp2/[ω(ω + iγ)] . Here, ω = 2πc/λ is the angular frequency of light in air, c is the light speed in vacuum, and λ is the light wavelength. ε∞, ωp, and γ stand for the relative permittivity at the infinite frequency, bulk plasma frequency, and electron collision frequency, respectively. For silver, these parameters can be set as ε∞ = 3.7, γ = 0.018 eV, and ωp = 9.1 eV [21–23]. The wavelength-dependent complex permittivity of monolayer MoS2 recently measured by Li et al. is employed in our calculations . The thicknesses of MoS2, SiO2, TiO2, spacer, and metal layers are set as do = 0.615 nm, ds = 110 nm, dt = 60 nm, dc = 250 nm, and da = 200 nm, respectively. The distance between the MoS2 and metal film is initially set as dm = 100 nm. First, we consider that the p-polarized light normally impinges on the structure (θ = 0). The light propagation characteristics in the multilayer can be studied numerically by the FDTD method. In FDTD simulations, the perfectly matched layer absorbing boundary condition is utilized on the right and left sides of computational domain. The periodic boundary condition is set at the bottom and top of the domain. The light absorption of MoS2 layer is calculated using AM = |Pl-Pr|/Pin in the simulations. Here, Pl and Pr are the light powers passing through the planes on the left and right of MoS2 layer, respectively. Pin is the incident light power.
3. Results and analysis
As shown in Fig. 1(b), the light absorption spectrum of the entire configuration with above geometrical parameters is achieved by the FDTD simulations. It is found that the absorption spectrum possesses a sharp peak at the visible wavelength of 662 nm, where the incident light is totally absorbed. This response in the hybrid photonic multilayer is regarded as Tamm plasmon polaritons . To theoretically confirm the numerical results, the transfer matrix method (TMM) can be used to calculate the light propagation features of the photonic multilayer . According to Maxwell’s equations and boundary conditions for electric fields between adjacent layers, the transfer matrixes separately characterizing the light propagation through the i-th boundary and i-th layer can be expressed asFig. 1(b).
Subsequently, we investigate the properties of light-matter interaction in monolayer MoS2 in the multilayer structure. As depicted in Fig. 2(a), the light absorption of MoS2 layer can be strongly enhanced and approaches ~96% at the absorption peak (λ = 662 nm) in Fig. 1(b), which is remarkable when compared with the previous reports [12–14]. This absorption efficiency is an order of magnitude higher than that of free-standing monolayer MoS2.The full width at half maximum of MoS2 absorption peak is ~11.5 nm, which contributes to the selective enhancement of MoS2 light absorption. The light absorption in the dissipative material (silver film) is about 3.2%, which is 1/30 of light absorption in MoS2 layer. To explore the mechanism of light absorption enhancement, we plot the electric field and intensity profile in the multilayer at λ = 662 nm obtained by FDTD simulations. The results in Fig. 2(b) illustrate that the electric field with 12-fold enhancement near the MoS2 layer is confined in the spacer (see Visualization 1), which contributes to the strong light-matter interaction in MoS2. The electric field is hardly enhanced (around 1 V2/m2) above the multilayer structure. This kind of strongly confined TP mode plays a crucial role in improving the light absorption of active materials . To make the physical mechanism clearer, we analyze the features of light absorption in monolayer MoS2. The light absorption of MoS2 layer can be calculated by the ratio of the absorbed power of MoS2 layer in the volume V to the input power passing through the MoS2 surface area S , which can be described asEq. (3). From Eq. (3), we can see that the light absorption of MoS2 layer is proportional to the electric field intensity in MoS2. By combing E(x,y) and ε”(x,y) in MoS2 layer at different wavelengths, we can obtain the light absorption of MoS2 layer, which is named as analytical result to differentiate from the simulation result. It is found that the analytical results are consistent with the numerical simulations, as depicted in Fig. 2(a).
The wavelength of TP mode is sensitive to the Bragg wavelength in the multilayer system . The layer thicknesses of dielectric Bragg grating will contribute to the tunability of MoS2 light absorption. Here, we study the light absorption response of monolayer MoS2 with different layer thicknesses of Bragg grating. As shown in Fig. 3(a), the wavelength of absorption peak for monolayer MoS2 exhibits a red-shift with increasing the thickness ds of SiO2 layer in the Bragg grating. From Fig. 3(b), we can see that the operating absorption wavelength of MoS2 maintains a nearly linear relationship with the SiO2 layer thickness. The FDTD results are consistent with TMM theoretical calculations. The position of TP mode is linearly dependent on the Bragg wavelength described as λB = 2(nsds + ntdt) . Thus, the above behavior of light absorption of MoS2 layer is understandable. Moreover, it can be seen in Fig. 3(b) that the light absorption of monolayer MoS2 drastically rises up, and then slowly falls down when ds increases. A maximum appears when ds approaches 110 nm. The analytical results calculated by Eq. (3) agree well with the FDTD simulations. As shown in Fig. 3(c), the electric field intensity around MoS2 layer is changed with the same field profiles in the spacer. The intensity nodes of electric field will move away from the spacer with the increase of ds. It is worth noting that the stronger field enhancement does not correspond to the stronger light absorption of MoS2 layer when ds is changed, as can be seen in Fig. 3(d). We find that ε” and electric field intensity of MoS2 layer together determine the light absorption of MoS2 layer. In the structure, the electric field intensity in MoS2 at the absorption peak changes in the opposite direction of the alternation of ε”. We further investigate the light absorption of monolayer MoS2 as a function of both ds and dt. The results illustrate that the MoS2 layer possesses the strongest light absorption when ds = 110 nm and dt = 60 nm, as shown in Fig. 3(e). As depicted in Fig. 3(f), the light absorption of MoS2 layer increases, and then decreases with increasing period number N when ds = 110 nm and dt = 60 nm. There is the maximal value (~96%) when N = 8, which may result in the approaching of critical coupling condition for MoS2 layer . When N>8, the critical coupling condition is not satisfied, giving rise to the decrease of MoS2 absorption.
We also investigate the dependence of light absorption of monolayer MoS2 on the position of MoS2 in the spacer. From Fig. 4(a), we can see that the light absorption of MoS2 layer is related to the distance dm between the MoS2 and metal film. The light absorption of MoS2 layer possesses the high value of >92% when dm falls in the range from 40 to 140 nm. As shown in the inset of Fig. 4(a), the maximum intensities of electric fields in the spacer with dm = 40 and 140 nm are larger than that of the spacer with dm = 100 nm. However, the intensity of electric field in MoS2 has a slight change, which gives rise to the high-efficiency light absorption of MoS2 in the structure with different dm. When dm = 200 nm, the light absorption of MoS2 layer reaches a smallest value, which results from the appearance of the trough of electric field around MoS2 in the structure, as shown in Fig. 4(b). Finally, we study the light absorption in monolayer MoS2 with different incident angles θ of light. It is found that the wavelength of absorption peak exhibits a blue-shift with the increase of θ, which contributes to the easy tunability of light-MoS2 interaction. Moreover, the MoS2 absorption peaks for s- and p-polarized incident light separate from each other, which derives from the splitting between the TE and TM TP modes in the multilayer . If the incident light is a Gaussian beam, the light absorption of MoS2 layer will be slightly influenced (see Fig. 5).
We have proposed a novel multilayer architecture consisting of a dielectric grating, a spacer, and a metal film on the substrate, and investigated the enhancement of light absorption of monolayer MoS2 in the spacer. The numerical and analytical results demonstrate that the light absorption of the atomically thin MoS2 layer can reach 96% with a narrow spectral width of 11.5 nm in the visible range due to the generation of highly-confined TP mode in the structure. The achieved nearly perfect light absorption is an order of magnitude higher than that of free-standing monolayer MoS2. The operating wavelength and efficiency of light absorption of monolayer MoS2 are particularly dependent on the layer thicknesses and period number of dielectric grating, MoS2 position, and incident angle of light, which are meaningful for the tunability and selectivity of light-MoS2 interaction. Our results can offer another excellent pathway for improving light absorption in 2D materials and MoS2 optoelectronic applications.
National Key Research and Development Program of China (2017YFA0303800); National Natural Science Foundation of China (11634010, 61705186, 11774290, 61377035, and 61575162); Natural Science Basic Research Plan in Shaanxi Province of China (2017JQ1023); and Fundamental Research Funds for the Central Universities (3102016OQD031).
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