Unique optical and electronic properties make molybdenum disulfide (MoS2) more attractive for its applications in sensing, catalysts, and optoelectronic devices ^[1–6]. As a novel semiconductor material, bulk MoS2 presents an indirect bandgap of 1.3 eV, while monolayer MoS2 exhibits a direct bandgap of 1.8 eV, which is demonstrated in theory ^[7]. Decreasing the thickness of MoS2 not only changes the bandgap, but also improves the photoluminescence (PL) intensity, which was detected experimentally ^[8]. Because of the distinctive optical properties of strong absorption and PL intensity, monolayer MoS2 shows better application prospects than does bulk MoS2. With the development of MoS2-based studies, more characterization techniques are required to further study the optical properties of monolayer MoS2.

Surface plasmon resonance (SPR) of a metal nanostructure largely enhances the light–exciton interaction in the near field, resulting in plasmon-enhanced phenomena such as Raman, fluorescence, and nonlinear effects ^[9–12]. Recent studies reveal that Ag core-SiO2 shell nanoparticles can greatly improve the fluorescence of exfoliated MoS2 sheets ^[13]. In core–shell nanostructures, the interaction distance between the emitter and metal has great impact on both PL intensity and fluorescence image. However, the ultrashort interaction distance is difficult to precisely control for actual core–shell substrates, leading to uncontrollable and unstable spectroscopy signals. Furthermore, optical image quality should be further improved by breaking the optical diffraction limit of the instrument. In this regard, the tip-enhanced spectroscopy (TES) configuration is the ideal substrate for the study of monolayer MoS2, in which scanning probe microscopy (SPM) is used to preciously control the metal tips ^[14,15]. More importantly, nano-spatial resolution can be offered by the TES technique, where the electromagnetic field energy is highly confined into the nanogap between the tip and the substrate ^[16,17].

Previous studies show both bulk and monolayer MoS2 can serve as the Raman substrates, where the former exhibits electromagnetic enhancement, while the latter utilizes chemical enhancement ^[18–20]. In addition, some efforts have been devoted to the optical properties of monolayer MoS2, such as PL, electroluminescence (EL), Raman scattering, and high-resolution optical images. Relevant studies demonstrate that the quantum effect and the coverage of metal nanoparticles intensely influence the nanoimage and molecular signal of MoS2 ^[21,22]. The crystal graphic orientation and structure defects of monolayer MoS2 can be identified by Raman spectroscopy and near-field PL images, respectively ^[23,24]. EL of monolayer MoS2 shows that the same excited state at 1.8 eV emerges in absorption, PL, and EL spectroscopies ^[25]. For TES of MoS2, there are still many unsolved scientific issues, such as the enhancement mechanism of MoS2-TES. Most studies of MoS2 were performed using the specific wavelength without considering wavelength scanning. However, wavelength-scanned TES results are of great importance to fully understand the spectroscopy properties of MoS2, and provide better guidance for experiments. Furthermore, radiative and nonradiative decay processes should be systematically studied to better understand the fluorescence properties of monolayer MoS2.

In this paper, we devote ourselves to studying the wavelength-scanned TES of monolayer MoS2 in theory for the first time, to the best of our knowledge. Dependence of Raman and fluorescence enhancements on the tip–MoS2-film distance was investigated by the three-dimensional finite-difference time-domain (3D-FDTD) method. The gap-mode TES provides huge enhancement factors (EFs) of Raman and fluorescence up to 4.5×108 and 3.3×103, respectively, at the optimal tip–MoS2-film distance of 1.0 nm. The fluorescence enhancement mechanism of monolayer MoS2 was studied in detail by analyzing the radiative and nonradiative decay rates, as well as the quantum yield in the presence of metal. Two cases involving Stokes shift and non-Stokes shift were respectively considered to discuss the fluorescence enhancement of monolayer MoS2. We believe the calculation results will be a good reference for not only better understanding the TES enhancement mechanism of monolayer MoS2, but also guiding the rational construction of MoS2-based optoelectronic devices with high efficiency.

Here, a TES configuration was chosen to study the Raman and fluorescence enhancement of monolayer MoS2. Figure 1 shows the calculated TES system, which consists of an Ag tip over the Ag substrate that is covered with monolayer MoS2. The side illumination mode is used where the electric field amplitude and incident angle of the p-polarized plane wave are 1.0 V/m and 60°, respectively. The apex radius and the full cone angle of the Ag tip are set as 15 nm and 20°, respectively. The thickness of MoS2 film is set as 1 nm. The tip–MoS2-film and tip–substrate distances are denoted by d and D, as shown in Fig. 1. The simulation region is set at 1000nm×1000nm×1000nm in 3D, and all boundaries adopt perfectly matched layer (PML) boundary conditions to avoid disturbance of the boundary reflection. Optical constants for silver and MoS2 were taken from the literature ^[26,27].

To quantitatively analyze the fluorescence enhancement mechanism of monolayer MoS2, the radiative and nonradiative decay processes were calculated by the 3D-FDTD method. Here, an electric dipole source was used to model the excited molecule that behaves as an oscillating electric dipole. The decay rate enhancement can be inferred from the relationship ^[28] where γ and P are decay rate and radiated power in the presence of the TES configuration. The subscript 0 shows that the molecule is in free space. In our calculations, we set two monitor boxes to collect the data of total and radiated power of the electric dipole in the TES system, and thus finally calculate the radiative (γr/γr,0) and nonradiative (γnr/γnr,0) decay enhancement. The relationship among the total (γtot/γtot,0), radiative, and nonradiative decay enhancement can be given as

Fluorescence enhancement arises mainly from the comprehensive contributions of excitation and emission processes. A localized plasmonic field can provide huge excitation enhancement (|M|2=|EL/E0|2, where EL and E0 are local and incident electric field, respectively) and radiative decay rate. The emission enhancement embodies the change of the quantum yield of monolayer MoS2 in the presence of a TES configuration. The quantum yield (Q) can be defined as

Therefore, we can define the fluorescence EF as where ωex and ωem are the excitation and emission frequencies, respectively. The details of the calculation method can be found anywhere ^[28–31].

Wavelength-scanned electric field enhancement (|M|2) offers clear characterization of the SPR properties of metal nanostructures from the near field. To clarify the SPR properties of TES, the Ag-tip–Ag-substrate-distance-dependent electric field enhancement of the TES configuration with (D=2nm) and without (D=1, 2 nm) monolayer MoS2 is presented in Fig. 2(a). The apex radius and the full cone angle of the Ag tip were set as 15 nm and 20°, respectively. For D=1nm [Fig. 2(a)], we observe a distinct SPR band around 650 nm that covers the resonance absorption of monolayer MoS2 ^[18,32]. In this case, the excitation rate of fluorescence was greatly enhanced by the SPR of the TES configuration. The SPR peak around 650 nm is assigned to the dipole coupling mode between the tip and the substrate. The obvious blueshift and decrease of |M|2 can be observed with the increase of D values (black and red lines). After the monolayer MoS2 was placed on the Ag substrate, larger |M|2 was observed (green line), implying greater Raman enhancement and excitation rate of fluorescence in the presence of monolayer MoS2.

In the TES configuration, the electric field enhancement was affected by many factors, such as the tip radius, the tip–substrate distance, the incidence angle of excitation light, and the vibration orientation of molecules. For example, a gold tip with optimal tip radius of 50–80 nm above a gold film provides maximum electric field enhancement. Of these variables, the tip–substrate distance has a dominating contribution to the tremendous electric field enhancement. More calculations were performed to further study the influence of tip–substrate coupling on the electric field enhancement of the TES configuration with monolayer MoS2 placed on the Ag substrate. Results demonstrate that |M|2 sharply decreases, and the SPR peaks blueshift with the increase of tip–MoS2-film distance from 1 to 4 nm [Fig. 2(b)], agreeing with the trend of a recent work ^[19]. In our simulations, the obtained electric field enhancement is defined as |M|2=|EL/E0|2, where EL is the local electric field. E0 is the incident field, and the value is set to 1.0 V/m by default. Therefore, the obtained EL is the EF of the electric field, and could clearly present the SPR properties of the TES system from the near field. The Raman EF is defined as |M|4, and, thus, the connections between the SPR properties and the Raman EF can be created by the wavelength-scanned |M|2. Figure 2(b) shows that maximum enhancement with resonance wavelength of 650 nm can be obtained at a tip–MoS2-film distance of 1 nm, giving a strong Raman enhancement of monolayer MoS2 as high as 4.5×108. The SPR band matches well the resonance absorption of monolayer MoS2 ^[18,32], implying larger excitation enhancement of fluorescence. All the above results indicate that larger electric field enhancement occurs at the shorter tip–substrate, distance offering larger plasmon coupling. However, no electric field enhancement is observed when the tip–substrate distance is 1 nm and the tip–MoS2-film distance is 0 nm. This is because the charge exchange occurs between the tip and the monolayer MoS2 film, which contact each other, leading to a decrease in field enhancement ^[33]. A side view of the normalized near-field distributions further support that fact [Figs. 2(c)–2(f)]. Calculation results display that “hotspots” are strongly localized in the nanogap between the tip and substrate under 660 nm laser excitation, which consequently offers a large Raman signal. Huge electric field enhancement on the surface of monolayer MoS2 film can also be observed from the top view, as shown in Fig. 2(g). No electric field enhancement at the junction between the tip and monolayer MoS2 film is observed at d=0nm [Fig. 2(c)].

In the above simulations, the Raman enhancement of monolayer MoS2 was quantitatively studied. Meanwhile, we have also analyzed the excitation enhancement (|M|2) of fluorescence. Aiming at understanding all fluorescence properties, it is essential to analyze the fluorescence emission of monolayer MoS2 in the presence of a tip. Figures 3(a)–3(c) show the 3D-FDTD calculated tip–MoS2-film-distance-dependent quantum yield, and the radiative and nonradiative decay rates. Simulation results reveal that the quantum yield is extremely sensitive to the tip–MoS2-film distance, indicating the strong influence of plasmon coupling on the fluorescence emission of monolayer MoS2 [Fig. 3(a)]. Decreasing the tip–MoS2-film distance will greatly improve the quantum yield, which achieves its maximum of 0.16 when d=1nm. We clearly observe distinct SPR peaks in the longer wavelength range (>600nm), because the radiative decay rate achieves its maximum in this region, leading to large enhancement in quantum yield [Fig. 3(b)]. In comparing Figs. 3(b) and 2(b), the SPR wavelength of the radiative decay rate matches that of the maximum electric field enhancement, which reveals that SPR in a TES system can significantly enhance the radiative decay process. It should be noted that the nonradiative decay rate dominates the fluorescence emission over the radiative part in the whole spectral region, indicating strong nonradiative energy transfer from the monolayer MoS2 to the TES system [Figs. 3(b) and 3(c)], and thus leads to low quantum yield. Both decay rates increase with the decrease of tip–MoS2-film distance. However, no enhancement in radiative decay rate could be observed when the tip–MoS2-film distance further decreases to 0 nm. In this case, the electric charge transfer between the tip and monolayer MoS2 reduces both radiative and nonradiative decay channels, while the nonradiative decay rate plays a dominate role in the whole fluorescence emission of monolayer MoS2, and thus leads to a lower quantum yield. Calculation results also indicate that greater tip–MoS2-film distance (>2nm) would cause quenching of fluorescence by the metal substrate, where the nonradiative decay rate dominates the fluorescence emission over the radiative part, as shown in Figs. 3(b) and 3(c).

Figure 3(d) shows the tip–MoS2-film-distance-dependent fluorescence EF of monolayer MoS2, plotted as a function of wavelength. Stokes shift between the emission and excitation wavelength was not considered. The calculation results demonstrate that the fluorescence EF sharply increases with the decrease of tip–MoS2-film distance ^[34]. A maximum EF as high as 3.3×103 can be achieved at the optimal distance of 1 nm, where the resonance band around 650 nm matches that of the electric field enhancement and quantum yield. Although the nonradiative decay rate dominates the fluorescence emission in the whole spectral region, the huge electric field enhancement [Fig. 2(b)] in the nanogap between the tip and the substrate efficiently overcomes the fluorescence quenching, and thus provides a great fluorescence EF of monolayer MoS2. No enhancement in tip-enhanced fluorescence (TEF) is observed because of the low quantum yield and excitation enhancement at tip–MoS2-film distance of 0 nm or >2nm. Appropriate tip–MoS2-film distance is required to obtain the strongest fluorescence enhancement. For larger gap distance (d>2nm), the fluorescence of monolayer MoS2 cannot be efficiently enhanced by the local electric field in TES configuration, but is quenched by the metal substrate. For shorter distance (d=0nm), both excitation enhancement and quantum yield decrease because of the electric charge transfer between the tip and MoS2 film, leading to decrease in the final fluorescence EF.

In the above discussion, the quantitative relationship between fluorescence EF and tip–MoS2-film distance was studied under the assumption that no Stokes shift between the emission and excitation wavelength was considered. However, in fluorescence measurements, the emission wavelength is always larger than the excitation wavelength, where Stokes shift should not be ignored. Figures 4(a) and 4(b) show the tip–MoS2-film-distance-dependent fluorescence EF under excitation wavelengths of 630 and 660 nm. The calculation results indicate that fluorescence EF increases sharply with the decrease of tip–MoS2-film distance from 4 to 1 nm. For d=1nm, we obtain maximum EF as high as 3 orders of magnitude at all emission wavelengths. Similar to the results of Fig. 3(d) for the shorter (d=0nm) and longer (d=4nm) tip–MoS2-film distance, no fluorescence enhancement is observed [insets in Figs. 4(a) and 4(b)]. Figure 4(c) show the tip–MoS2-film-distance-dependent fluorescence EF at emission wavelength of 680 nm, where the excitation wavelengths were set at 630 and 660 nm. As the tip–MoS2-film distance increases from 0 to 1 nm, the fluorescence EF improves rapidly, and then decreases sharply with further increase of the tip–MoS2-film distance ^[34]. The fluorescence EF achieves its maximum at tip–MoS2-film distance of 1 nm, showing fluorescence EF of 3 orders of magnitude. To find the optimal excitation wavelength, we calculated the dependence of fluorescence EF on tip–MoS2-film distance, with the emission wavelength set at 680 nm [Fig. 4(d)]. The fluorescence EF decreases with the increase of tip–MoS2-film distance and the maximum EF of 3 orders of magnitude is obtained at distance of 1 nm, showing the optimal excitation wavelength of 650 nm. Similarly, no fluorescence enhancement is observed when d=0nm and d=4nm, where the values are multiplied by 100 and 10, respectively.

Our calculation results show that both Raman and fluorescence enhancement are extremely sensitive to the tip–MoS2-film distance. The feasibility of the experiment should be considered because the tip–film distance is always less than 1 nm by traditional manipulation of a SPM tip that depends on the bias voltage and tunneling current between the tip and film. However, in most TES instruments, a piezoelectric ceramics tube can be used to offer precise nano-positioning control. The shift of the piezoelectric ceramics tube is controlled by the applied voltage. We can set up appropriate voltage to achieve precise tip–film distance from 1 nm to micrometer scale.

Theoretical simulations have been done to study TES of monolayer MoS2. 3D-FDTD results show that Raman and fluorescence enhancement can be as high as 8 and 3 orders of magnitude, respectively, at the optimal tip–MoS2-film distance of 1 nm. Study of monolayer MoS2 fluorescence demonstrates that decreasing the tip–MoS2-film distance will greatly improve the quantum yield, achieving its maximum of 0.16 when d=1nm. Huge electric field enhancement in the nanogap between the tip and the substrate can efficiently overcome the fluorescence quenching, and thus provides great fluorescence EF of monolayer MoS2. No enhancement in TES is observed when d=0nm because of the charge transfer between the tip and the monolayer MoS2 film.