The light absorption of a hybrid novel MoS2-based nanostructure is theoretically investigated by using the finite-difference time-domain (FDTD) simulations, and high-efficiency broadband absorption is achieved in the visible wavelength region. The enhancement of localized electromagnetic field owing to that localized surface plasmon resonances (LSPRs) supported by Au nanoparticles (NPs) can be used to enhance the absorption of MoS2, and the localized absorption of monolayer MoS2 are remarkably enhanced up from about 18.3% and 4.6% to about 55.2% and 84.8% at the resonant wavelengths of 467.7 nm and 557.8 nm, respectively. Furthermore, the effects of radii of Au NPs, period of Au NPs array, Au@Si NPs core-shell ratios, period numbers of the distributed Bragg mirror (DBR), and incident angle on the absorption of the proposed nanostructure have been systematically investigated. The similar design idea to enhance the light-MoS2 interaction can also be applied to other transition-metal dichalcogenides (TMDCs). This work will contribute to the design of TMDCs-based nanophotonic and optoelectronic devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Two-dimensional (2D) materials, such as graphene [1–3], hexagonal boron nitride (hBN) , and transition-metal dichalcogenides (TMDCs) [5–7] have received an upsurge of attention for application in nanophotonics and optoelectronics owing to their unique electrical, optical and mechanical properties. Unlike graphene, TMDCs (e.g., MoS2, MoSe2, WS2, and WSe2) possess special direct band gaps and internal amplification similar to semiconductors. Furthermore, molybdenum disulfide (MoS2) attracts more attention than other TMDCs due to the relative abundance of molybdenum crystals . As a typical kind of TMDCs, MoS2 has high current cut-off ratios  and tunable optical and electronic properties , these unique characteristics make MoS2 an excellent candidate to realize photonic functional devices, such as field-effect transistors [11,12], photoluminescence devices [13,14], photodetectors [15,16], and photovoltaic devices [17,18]. However, the absorption of monolayer MoS2 is usually lower than 0.1 within the visible wavelength region  owing to the ultra-thin thickness, which limits its potential applications in many optoelectronic devices. Therefore, the enhancement of absorption in monolayer MoS2 acts as a greater role in enabling MoS2-based optoelectronic devices.
Over the past few years, many efforts have been made to enhance the absorption of monolayer MoS2. It is well known that the common method is utilizing resonances to enhance absorption [20–27], however, the monolayer MoS2 does not have strong resonant behavior in the visible range. Therefore, the monolayer MoS2 is usually inserted into the designed resonant structure to use the resonance in the structure enhancing the absorption. Liu et al.  combined a photonic crystal slab with a spacer to enlarge the absorption of monolayer MoS2 to 0.35. Guo et al.  proposed a magnetic coupling metasurface to achieve the broadband absorption enhancement in the monolayer MoS2. Long et al.  made full use of Ag grating to enhance the optical absorption of monolayer MoS2 by mechanism of magnetic polariton (MP), and the maximum absorption of the monolayer MoS2 layer itself is increased by more than 20-fold to nearly 90%. Lu et al.  proposed a novel multilayer photonic structure to realize the strong optical absorption in monolayer MoS2 due to the excitation of Tamm plasmon polaritons (TPP). The critical coupling of guided resonances in the photonic crystal slab combined with metallic or multilayer Bragg reflectors have also been reported to acquire high absorption of light in monolayer MoS2 [32–34].
Furthermore, another effective approach to enhance and control the optical response of materials relies on the use of localized surface plasmon resonances (LSPRs) sustained by metal nanoparticles (NPs) . LSPRs is collective oscillations of the conductor’s surface electrons at the interface between the metal NPs, which are much smaller than the incident light wavelength, and a dielectric medium under excited electromagnetic field that tends to trap optical waves near their interface . LSPRs wavelength of Ag and Au NPs can be effectively tuned by size, shape, and surrounding dielectric medium . Yang et al.  investigated the optical properties of monolayer MoS2/Ag NPs hybrids and their application to surface catalytic reactions. Britnell et al.  enhanced light absorption within monolayer MoS2 which was spattered on top of Au NPs, and observed a 10-fold increase in the photocurrent at wavelength of 633 nm. Sobhani et al.  employed Si-core Au-shell NPs with a surface coverage of less than 1% and demonstrated a 3-fold increase in the photocurrent and a 2-fold increase in the photoluminescence at the excitonic transitions of 630 and 680 nm of MoS2 near the band edge. However, the localized absorption of monolayer MoS2 in previous studies is not sufficient enough for optoelectronic devices, which needs to be significantly enhanced over the visible wavelength. To tackle this problem, broadband light absorption structure should be developed for monolayer MoS2 so that it can be more efficiently applied to solar energy conversion devices and broadband photodetectors.
In this study, we propose a MoS2-based nanostructure that can enhance the localized absorption of monolayer MoS2 based on LSPRs supported by Au NPs. The novel MoS2-based nanostructure is composed of a periodic Au NPs array, a distributed Bragg mirror (DBR) with alternate silicon dioxide (SiO2) and silicon (Si) layers, and a monolayer MoS2 is sandwiched between the periodic Au NPs array and DBR. Actually, using DBR as a substrate can greatly suppress the light pass and reflect the incident light for reabsorption. Therefore, combining Au NPs array and DBR can achieve localized field concentration to further enhance the localized absorption of monolayer MoS2. Consequently, high-efficiency broadband localized absorption of the MoS2-based nanostructure can be achieved, and the localized absorption of monolayer MoS2 in the wavelength range from 400 nm to 700 nm can be obviously improved. Meanwhile, such a MoS2-based nanostructure enables tunable operating wavelength by adjusting the geometrical parameters to realize the wavelength selectivity of the system. Moreover, such a kind of plasmon-enhanced MoS2-based nanostructure can also be extended to other monolayer TMDCs, such as WS2, MoSe2 and WSe2, which demonstrates that plasmon-enhanced MoS2-based nanostructure is of general applicability for high-efficiency light absorption within 2D materials. The meaningful improvement and tunability of the absorption in 2D materials can be applied to 2D materials-based optoelectronic devices.
2. Structure and modeling method
As shown in Fig. 1, the proposed MoS2-based nanostructure consists of a periodic Au NPs array, a DBR composes with alternate SiO2 and Si layers with a period number of N, and a monolayer MoS2 is sandwiched between the periodic Au NPs array and DBR. The Au NPs array is periodic in the x- and y-directions, and the period can be expressed as Px and Py, respectively. In this study, we only consider the absorption as P = Px = Py for simplification. The dielectric function of Si and SiO2 can be obtained from Ref , and the thickness d1 and d2 of Si and SiO2 can be set as d1 = 38 nm and d2 = 90 nm, respectively. A plane electromagnetic wave is normally incident from air to the periodic Au NPs array. In our calculation, the wavelength-dependent complex dielectric function of the monolayer MoS2 has been measured experimentally by Li et al.  and the thickness of monolayer MoS2 is set as 0.65 nm. Simultaneously, the dielectric function of Au is derived from Palik . The finite-difference time-domain (FDTD) simulations are utilized to numerically calculate the light absorption of the proposed MoS2-based nanostructure. In the simulations, the perfectly matched layer absorbing boundary condition is applied along the z-direction, and the periodic boundary condition is employed in the x- and y-directions, respectively. In addition, the non-uniform mesh is adopted, and the minimum mesh size inside the monolayer MoS2 equals to 0.1 nm and gradually increases outside the MoS2 sheet for saving storage space and computational time.
3. Results and discussion
Figure 2(a) manifests the simulated absorption spectra of a suspended monolayer MoS2, a periodic Au NPs array, a periodic Au NPs array on monolayer MoS2 and the proposed MoS2-based nanostructure for normal TM-polarized light (magnetic field is perpendicular to the x–z plane) in the wavelength region from 400 nm to 700 nm. Here, unless a specific description, the basic geometrical parameters are assumed as r = 39 nm, P = 100 nm, d1 = 38 nm, d2 = 90 nm and N = 5. The band structure and carrier density of the monolayer MoS2 determine its optical absorption. Actually, monolayer MoS2 has a large absorption coefficient, while it is too thin so that a suspended monolayer MoS2 can be regarded as transparent especially at the visible wavelength region, the average absorption is about 0.1 in the wavelength range from 400 nm to 700 nm. The maximum absorption of a suspended monolayer MoS2 is 0.23 at near 435 nm, and two small peaks, which can be attributed to the excitons transitions, exist with absorption peak about 0.06 at near 606 nm and 658 nm. For the periodic Au NPs array, the absorption in short wavelength range reaches above 0.4, which is higher than that in long wavelength range, and an absorption peak exists at wavelength of near 510 nm owing to the excitation of LSPRs. For a periodic Au NPs array on monolayer MoS2, compared with the absorption of the suspended monolayer MoS2, the absorption of the whole structure at the given wavelength region is obviously improved. The maximum absorption is about 0.56 at near 430 nm, and two small peaks exist with absorption about 0.17 at near 606 nm and 658 nm. In addition, a new absorption peak occurs at near 505 nm owing to the intrinsic absorption property of Au NPs array. However, the localized absorption of monolayer MoS2 with the help of the above nanostructure at the given wavelength region is still weak.
Therefore, a DBR is introduced to enhance the absorption of MoS2, because DBR just serves as a mirror to effectively reflect light back for reabsorption and has little effect on the pattern of the optical electric in the device, and the reflection spectra of DBR is shown in Fig. 2(b). It is well known that the high reflectivity of DBR can increase the light pass through monolayer MoS2, and the combined influence of DBR and Au NPs array increases the light pass through monolayer MoS2, and achieves localized field concentration to enhance the absorption of monolayer MoS2. Then, the absorption of the proposed MoS2-based nanostructure can be described by , where and are the reflection and transmission spectra of the proposed nanostructure. The pink line in Fig. 2(a) shows the absorption of the proposed MoS2-based nanostructure, and the absorption is obviously improved. It is found that the absorption of the proposed MoS2-based nanostructure can achieve above 0.99 at the wavelengths of 467.7 nm and 557.8 nm. Differently, the absorption peaks of the excitons are covered owing to the existence of the DBR . In order to calculate the localized absorption by the MoS2 in the proposed MoS2-based nanostructure, the power dissipation density can be given as follow [43,44]Fig. 2(a) manifests the localized absorption of monolayer MoS2 in the wavelength range from 400 nm to 700 nm, and the localized absorption is obviously improved. From the point of macroscopic electromagnetism, we give an analysis of near-perfect absorption based on the impedance transformation method. When the near-perfect absorption condition is satisfied, the impedance of the nanostructure should be equal to that of the free space (Z0 = 1). The relation between the S parameters and impedance Z can be expressed as [45,46]
The relation between the impedance Z of the proposed MoS2-based nanostructure and the wavelength is plotted in Fig. 2(c). It is well known that, in order to obtain a near-perfect absorption, the impedance at the wavelength of the working band should match the free-space impedance, namely Z (λ) = Z0 (λ) [45,46]. Results show that the impedance Z of the proposed MoS2-based nanostructure is close to unity at the wavelengths of 467.7 nm and 557.8 nm, which agree well with the near-perfect absorption wavelengths shown in Fig. 2(a), namely, the well impedance matching indeed is achieved. Moreover, in order to further elucidate the underlying physical mechanism, the electric and magnetic field amplitude distributions at the resonant wavelengths of 467.7 nm and 557.8 nm are given in Figs. 3(a)-3(d) under the normal TM-polarized light whose electric field along the x-z plane. Consequently, the electric and magnetic fields around the surface of Au NPs are gathered and enhanced. In fact, such electromagnetic field characteristics correspond to the excitation of LSPRs mode. In other words, the incident electric and magnetic field are trapped surrounding the monolayer MoS2 due to that LSPRs induces light energy concentration and near field enhancement.
Subsequently, we further investigate the dependence of the absorption of the proposed MoS2-based nanostructure on geometrical parameters. First, we discuss the effect of the period number N of the DBR on the absorption owing to that DBR can act as a back reflector and effectively suppress the transmission of light. As shown in Fig. 4(a), results illustrate that increasing the period number N of the DBR can promote the absorption of light, and when the number of period , the absorption at the given wavelength region almost reaches saturation condition. This can be attributed to that the optical reflectivity of the inserted DBR achieves the saturated value, the corresponding reflection spectra of the DBR is shown in Fig. 2(b). As we know, LSPRs wavelength of Au NPs can be effectively tuned by size, shape, and surrounding dielectric medium . Then, we explore the influences of changing the radii of Au NPs on the optical absorption of the proposed MoS2-based nanostructure, as shown in Fig. 4(b). Since LSPRs can harvest electromagnetic energy and significantly promote the absorption, the radii of Au NPs have a remarkable influence on LSPRs . It can be seen from Fig. 4(b) that when we increase the radii of Au NPs, the absorption spectrum obviously moves into a longer wavelength, the absorption peaks at the resonance wavelength almost reach unity at r = 39 nm, and then the absorption at the resonance wavelength will slightly diminish when r continuously increases or decreases. Similarly, Fig. 4(c) shows the effect of the period of Au NPs array on the absorption spectra of the proposed MoS2-based nanostructure. Altering the period of Au NPs array from 100 nm to 120 nm, the absorption spectrum moves into a shorter wavelength, and the absorption at the resonant wavelength will decrease with the period increasing, which can be attributed to that LSPRs will weaken between Au NPs with the period of Au NPs array increasing.
In addition, the above calculations are just based on normal incident light. However, an ideal absorber should satisfy high optical absorption to work on the relatively wide range of incident angles in the practical applications of nanophotonic and optoelectronic devices. As a result, we further investigate the optical absorption of the proposed MoS2-based nanostructure with different incident angles in order to explore the absorption dependence at oblique incidence under TM and TE polarizations, and results are shown in Figs. 5(a) and 5(b), respectively. It can be seen that the absorption of the proposed MoS2-based nanostructure is almost independent with the incident angle increasing from 0° to 30° for both TM and TE polarizations, which can be attributed that LSPRs coupling can be maintained for TM or TE polarized incident light with small incident angles. This provides a quite suitable way to optimize the absorption at the concerned wavelength region by just adjusting the incident angle. Therefore, the polarization-insensitive property, combined with the good absorption stability under oblique incidence, undoubtedly enables this absorber to be more feasible in practical applications of nanophotonic and optoelectronic devices.
Moreover, it has been demonstrated that core-shell NPs insulated by a shell, which can be called core-shell NPs. The hybrid core-shell NPs can lead to a better photovoltaic performance than bare metal NPs, which can be attributed to that the shell not only ensures electrical and chemical isolation of the plasmonic core, but also provides another possibility to tune LSPRs owing to that it is dependent on the dielectric function of the surrounding medium . Here, we investigate the impact of different Au@Si NPs core-shell ratios on the absorption of the proposed MoS2-based nanostructure, as shown in Fig. 6. Results manifest that the introduction of the coating shell can increase the light absorption wavelength bandwith compared with the bare Au NPs. Two absorption peaks occur in the absorption spectra, and the absorption peak at the wavelength of about 467 nm is the result of coupling between MoS2 and Au@Si NPs, and almost unchanged with core-shell ratios increasing, of which the absorption contribution of MoS2 is dominant. However, the second absorption peak is mainly the contribution of the Au@Si NPs, and the absorption peak gradually moves into a longer wavelength with the increasement of core-shell ratios. It is noted that, in experiments, Au NPs typically have a layer of organic ligands attached on their surface, the layer could be one or several nanometer in thickness, thus the above nanostructure can be regarded as a simple core-shell structure.
In the end, we try to make use of the proposed nanostructure to enhance the optical absorption of other TMDCs, such as WS2, MoSe2 and WSe2, of which the MoS2 is replaced by other TMDCs in the proposed MoS2-based nanostructure. Simulated absorption spectra for the proposed nanostructure of monolayer WS2, MoSe2 and WSe2 are shown in Figs. 7(a)-7(c), respectively, and geometrical parameters are similar to that used in Fig. 2(a). In our calculation, the dielectric function of WS2, MoSe2 and WSe2 are obtained from the experimental measurement of Li et al. , and the corresponding thicknesses are set as 0.618 nm, 0.646 nm and 0.649 nm, respectively. It should be pointed that the optical properties of monolayer TMDCs can be influenced by their environment (substrate, any layers on top, etc.) and carrier doping concentrations in experiments. Compared with the single-pass absorption spectra (black lines) of monolayer TMDCs suspended in air, the absorption performance (blue lines) of monolayer TMDCs based on our proposed TMDCs-based nanostructure can be obviously improved. Undoubtedly, because WS2, MoSe2 and WSe2 are similar to MoS2, we can also change the operating wavelength by altering the geometrical parameters to achieve the wavelength selectivity of the system, such as period of Au NPs array, radii of Au NPs, and period numbers of the DBR or Au@Si NPs core-shell ratios. Consequently, the proposed TMDCs-based nanostructure with its unique design principle can provide a new approach to improve light absorption of various monolayer 2D materials.
In this study, a hybrid novel MoS2-based nanostructure is proposed to utilize LSPRs supported by Au NPs to obtain high-efficiency broadband localized absorption for a monolayer MoS2. It is proved that the combined influence of DBR and Au NPs array can increase the light pass through monolayer MoS2 and achieves localized field concentration to enhance the absorption of monolayer MoS2. The absorption of the MoS2-based nanostructure can reach above 99%, and the corresponding localized absorption of MoS2 at the resonant wavelengths of 467.6 nm and 557.8 nm can be respectively improved from about 18.3% and 4.6% to about 55.2% and 84.8%. The significant enhancement of monolayer MoS2 absorption in the MoS2-based nanostructure can be acquired for both TM and TE polarizations. In addition, a further investigation reveals that the absorption of the MoS2-based nanostructure can be flexibly tailored by altering the geometrical parameters and incident angle, which is of great practical significance to improve the efficiency and selectivity of the absorption in monolayer MoS2. Similar results can also be acquired for other TMDCs, such as WS2, MoSe2 and WSe2. This work will contribute to the design of TMDCs-based nanophotonic and optoelectronic devices.
National Natural Science Foundation of China (NSFC) (51676077, 51776078, 51827808, 51806070); Fundamental Research Funds for the Central Universities (2016YXZD009); China Postdoctoral Science Foundation (2018M632849); Shenzhen Basic Research Project (JCYJ20170307171534237); National Basic Research Program of China (2015CB251505).
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