1. Introduction

The tunnel junction of a scanning tunneling microscope (STM) is an interesting configuration to address light-matter interaction at the nanoscale. The light emitted or absorbed by the junction provides great insight into the fundamental interaction processes between light and the tunnel junction itself or with a quantum system placed in the gap between the tip and the surface. The inelastic electron tunneling across the gap can excite localized surface plasmon modes generated by the close tip-surface proximity, giving rise to electroluminescence. The emitted light not only carries information about the radiative electromagnetic modes of the nanocavity but also about the tunneling electron energy distribution [1–5]. Theoretical models were used to interpret the intensity and spectral distribution of the observed light emission [6–9]. A quantum emitter (organic molecules, quantum dots or monolayer thick materials) located in the gap can modify the electromagnetic environment surrounding the STM junction. The inelastic tunneling through the quantum emitter can induce light emission [10–17]. The excitonic emission produced by a TMD monolayer in an STM [18–22] can be enhanced by plasmonic modes localized in the cavity. The plasmon-exciton interaction has been widely addressed in various hybrid TMD/plasmonic systems [23–31]. However, their interaction in an STM junction has just been investigated experimentally [19,20,32].

In this work, we investigate, by numerical simulations, the light-matter interaction of a hybrid metal/semiconductor tunneling junction where an $MoSe_2$ monolayer lays on a gold substrate which forms a plasmonic cavity with a gold tip. Using an incident optical excitation as a probe, we are able to reveal the surface plasmon modes strongly localized within the tunnel junction and their interaction with the excitons confined in the $MoSe_2$ layer. The effect of STM electron tunneling on the optical properties is taken into account using the Quantum-Corrected Model introduced by Esteban et al. [33]. The resonance frequency and strength of the nanogap modes are tuned by the main tunneling parameters, namely the tip-surface distance and the bias voltage applied to the junction. We address as well the roles of the incident polarization and of the optical anisotropy of the $MoSe_2$ layer. In particular, we investigate the nature and strength of plasmon-exciton coupling and its dependence on tip-surface distance and applied bias voltage.

2. Methods

The electromagnetic modes excited in purely metallic and hybrid metal/TMD junctions are studied by means of numerical electrodynamic simulations based on the Discrete Dipole Approximation (DDA) method [34]. Their optical spectra properties, spatial localization and dependence on the main tunneling parameters (tip-surface distance and bias voltage) are computed.

DDA is used to calculate approximated solutions to Maxwell’s equations thus providing access to the near-field and far-field optical properties of a given target. The latter is modeled by a 3D-array of polarizable point dipoles, whose polarizabilities are given by the position and frequency dependent dielectric function $\epsilon (\textbf {r},\omega )$ of the constituting materials.

Figure 1 presents the hybrid metal/TMD junction studied in this work where a gold STM tip is approximated by a revolution hyperboloid with a length of $15$ nm and an apex radius of $0.15$ nm. This tip is located over a $20$ nm $\times$ $20$ nm $\times$ $2.2$ nm gold substrate. An $MoSe_2$ monolayer simulated by a $0.8$ nm-thick [35] rectangular brick is supported by the metallic substrate with no gap between the two media. For gold, we use the complex refractive index tabulated by Johnson and Christy [36]. For the $MoSe_2$ monolayer, we use both isotropic and anisotropic optical refractive indices (see below). The distance between the gold tip and the $MoSe_2$ layer varies from 0.2 nm to 2 nm. The inter-dipole spacing is set to 0.1 nm which ensures a full convergence of the calculations while keeping within a reasonable computation time.

 

Fig. 1. Schematic representation of the simulated hybrid $Au/MoSe_2/Au$ tunneling junction: (A) tip-sample junction composed of the gold tip and the $MoSe_2$ monolayer deposited on the Au substrate. It is excited by a linearly p- or s-polarized electromagnetic wave (pink and green arrows respectively). (B) In the tunneling regime ($l < 0.5$ nm), the Quantum Corrected Model (QCM) is used and the conducting effective medium is modeled by a set of cylindrical shells with a gap distance dependent conductivity.

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The optical response of this hybrid $Au/MoSe_2/Au$ tunneling junction excited by an incident optical wave is computed. The asymmetry of the junction’s geometry leads to a polarization-dependent optical response which is investigated using p- and s-polarized incident light (see Fig. 1). The incident wavevector is impinging on the $MoSe_2$ monolayer at 45$^\circ$ angle with respect to the tip axis. The p-polarization vector has two components, orthogonal and parallel to the tip axis, and the s-polarization vector is parallel to the $MoSe_2$ surface.

The tip-surface gap distance $l$ is one of the key parameters of the tunnel junction. In their work, Esteban et al. [33] distinguished three regimes: (i) the non-tunneling regime ($l\ge 0.5$ nm) , (ii) the quantum tunneling regime ($0.5$ nm $> l >0.1$ nm) where gap plasmon modes are spectrally and spatially impacted by electron tunneling, and (iii) the contact regime ($l\le 0.1$ nm) where charge transfer leads to strong modifications of the tip-surface optical properties.

Here, we investigate the optical properties of the $Au/MoSe_2/Au$ STM junction in the non-tunneling regime ($l\geq 0.5$ nm) and in the tunneling regime ($0.5$ nm $> l\ge 0.2$ nm). In the latter case, we use the Quantum-Corrected Model (QCM) introduced by Esteban et al. [33]. QCM implements nonlocal and quantum effects within classical electrodynamic calculations thus significantly reducing the computing load compared to fully quantum mechanical calculations. In our QCM-DDA simulations, an effective medium is introduced between the tip and the monolayer and consists in a set of cylindrical homogeneous shells which account for tunneling across the tip-surface gap (see Fig. 1). Each shell is characterized by a gap distance and bias voltage dependent permittivity $\epsilon _g(l,V,\omega )$ given by:

3. Results and discussion

3.1 Non-tunneling regime

To get started, the optical response of the $Au/MoSe_2/Au$ junction to an excitation by an incident electromagnetic wave is studied in the non-tunneling regime. For this purpose, a sufficiently large gap is considered $\left ( l=0.5\,nm\right )$ so that electron tunneling and the quantum corrections are negligible. The optical properties of a purely metallic $Au/Au$ junction with the same tip-surface gap distance is also investigated for comparison.

Figure 2 shows the spectra of the average electric near-field enhancement calculated in the case of a purely metallic Au/Au junction for p- and s-polarizations. For p-polarization, the field enhancement is averaged over a volume that includes the gap, the tip apex and part of the substrate. For s-polarization, it is averaged over a plane perpendicular to the tip apex and placed within the substrate. Both spectra present an intense peak: at $710$ nm for p-polarization and at $620$ nm for s-polarization. Furthermore, both spectra exhibit a shoulder: at $575$ nm for p-polarization and at $530$ nm for s-polarization. Near-field enhancement maps have been computed to identify the electromagnetic mode corresponding to each peak (see Supplement 1).

 

Fig. 2. Average electric near-field enhancements of the $Au$/$Au$ junction calculated for s and p- incident polarizations. For p-polarization (dotted line), the averaging volume includes the gap, the tip apex and part of the gold substrate. For s-polarization (continuous line), the averaging is performed over a finite plane perpendicular to the tip axis and located within the substrate at $0.4$ nm from its upper surface. The tip-surface distance is $l=0.5$ nm.

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The vertical component of the p-polarized field efficiently excites the longitudinal tip-surface plasmon modes, the so-called dipolar gap plasmon modes [40,41]. According to the electric near-field enhancement map of Figure S1 in Supplement 1, the peak centered at $710$ nm in Fig. 2 is assigned to such a gap plasmon resonance. The shoulder at $575$ nm is assigned to transverse (with respect to the tip axis) plasmon oscillations of the tip and the substrate, excited by the horizontal component of the p-polarization. At this tip-surface distance, higher order gap plasmon modes are not excited in the investigated spectral range [33,42]. For s-polarization, the peak at $620$ nm corresponds to the dipolar transverse localized surface plasmon resonance (LSPR) of the substrate (see Figure S2 in Supplement 1). The weak shoulder at $530$ nm is attributed to the transverse LSPR of the tip. The gap plasmon resonance is about 10 times more intense than the transverse LSPR of the substrate due to the strong localization of gap plasmon modes.

We now focus on the $Au/MoSe_2/Au$ hybrid junction. First, we investigate its optical properties in the non-tunneling regime $\left ( l=0.5\,nm\right )$. Due to its atomically layered structure, the $MoSe_2$ monolayer exhibits highly anisotropic in- and out-of-plane optical indices [43]. In Fig. 3, we compare the optical responses calculated considering both isotropic and anisotropic $MoSe_2$ optical indices. The permittivity of the isotropic $MoSe_2$ as well as the in-plane permittivity component of the anisotropic $MoSe_2$ layer are taken from the measurements of Liu et al. [44]. The out-of-plane permittivity component of the anisotropic $MoSe_2$ is from Beiranvand [45] calculations (see Figures S3 and S4 in Supplement 1).

 

Fig. 3. Near-field optical response of the $Au/MoSe_2/Au$ junction in the classical regime $\left ( l=0.5\,nm\right )$. (A-B) Spectra of the average electric near-field enhancement calculated for p- and s- incident polarizations. For p-polarization, the averaging volume includes the gap, the tip apex and part of the $MoSe_2$ layer. For s-polarization, the average is calculated over a plane normal to the tip axis and located within the $MoSe_2$ monolayer at $0.4$ nm from its upper surface. The green arrows indicate the dips at the A and B exciton absorption wavelengths. The continuous and dotted lines show the spectra calculated using an anisotropic and isotropic refractive index for $MoSe_2$ layer, respectively. (C-D) Electric near-field enhancement maps calculated in the yz plane. The junction is illuminated (C) by a p-polarized incident light at $\lambda =710$ nm (in log scale) and (D) by a s-polarized incident light at $\lambda =800$ nm. The $MoSe_2$ layer is described by an anisotropic dielectric function.

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In order to investigate the gap plasmon modes excited in the hybrid junction, we calculate for p-polarization, the average electric near-field enhancement over a volume that includes the gap region, the tip apex and part of the $MoSe_2$ layer. We observe that the calculated spectra (Fig. 3(A)) are very similar to the one obtained for a purely metallic junction (Fig. 2). The field enhancement map in Fig. 3(C) shows that the main part of the induced electric near-field is concentrated between the tip apex and the $MoSe_2$ layer [41,46]. The maximum local-field intensity enhancement is located under the tip apex and reaches a value of about 450 for an anisotropic $MoSe_2$ layer.

For s-polarization, the electric near-field enhancement is averaged over a plane perpendicular to the tip axis and located within the $MoSe_2$ layer. The so-obtained spectra (Fig. 3(B)) are drastically different from the one obtained for the purely metallic $Au/Au$ junction (Fig. 2). Because of the presence of the $MoSe_2$ layer, the peak located at $620$ nm in the case of the $Au/Au$ junction (Fig. 2) has red-shifted and now overlaps with the A and B excitonic resonances of the $MoSe_2$. This results in a Fano-type interference between the plasmonic and the excitonic resonances [27–29]. Such interference is responsible for the asymmetric lineshapes shown in Fig. 3(B) characterized by two spectral dips at the A ($800$ nm) and B ($700$ nm) excitons absorption wavelengths. The dip at the A-exciton wavelength is more pronounced due to the smaller damping of A-excitons compared to B-excitons [47]. The near-field enhancement map is plotted in Fig. 3(D) for s-polarization at the A-exciton absorption wavelength. The electric field is fully located within the $MoSe_2$ layer and the $Au$ substrate with a maximum at the $MoSe_2$/$Au$ interface. This induced local electric field corresponds to a hybrid plasmon-exciton mode with a clear interface character in agreement with previous results [19]. It is due to the effective coupling between the $MoSe_2$ excitons and the transverse LSPR substrate modes (Figure S2 in Supplement 1). For p-polarization, the near-field spectra obtained (see Fig. 3(A)) do not present any indication of plasmon-exciton coupling because the field enhancement is calculated over a volume that does not include the $MoSe_2$/$Au$ interface. If a larger averaging volume is considered, the plasmon-exciton coupling would be taken into account and one may observe the Fano-interference in the near-field spectra. The plasmon-exciton coupling is hardly visible in the near-field enhancement map for p-polarization (Fig. 3(C)) but will appear more clearly for larger tip-surface distance (see discussion below).

By comparing isotropic and anisotropic spectra (Fig. 3(A-B), we observe, for p-polarization, a reduction of the peak intensity at $710$ nm and a slightly larger full width at half maximum (FWHM) when the $MoSe_2$ layer is isotropic. As a matter of fact, the gap plasmon mode is damped when the $MoSe_2$ layer is introduced in the gap since it is an absorbing medium at the gap plasmon wavelength. This damping is stronger when an isotropic $MoSe_2$ optical index is used because its corresponding damping factor is larger than the one of the out-of-plane anisotropic $MoSe_2$ (see Fig S3 and S4 in Supplement 1). In the same way, for s-polarization, the observed plasmon-exciton coupling is also damped when the out-of-plane permittivity of the $MoSe_2$ layer is significant. Compared to the actual anisotropic case, the use of an isotropic refractive index for the $MoSe_2$ layer leads systematically to a stronger damping of electromagnetic modes in the hybrid $Au/MoSe_2/Au$ tunnel junction. Henceforth, we will use the anisotropic dielectric function to describe the $MoSe_2$ layer.

3.2 Tunneling regime

In this section, we investigate how the near-field optical response of the junction changes when the QCM [33,42] is included in the DDA simulations. The tip-surface gap distance is set to $l=0.2$ nm and the applied bias voltage to $V=2$ V.

Figure 4 shows the average electric near-field enhancement spectra obtained for p- and s-polarizations with and without quantum corrections. For p-polarization (Fig. 4(A)), when the QCM is applied, the expected redshift of the gap plasmon resonance due to the introduction of an effective medium in the gap region (see Fig. 1) is negligible. This is due to the fact that the refractive index of this effective medium is very close to 1, the static conductivity $\sigma (l,V)$ being very small ($\sigma (l,V) < 5$ S.m$^{-1}$) compared to $\omega \epsilon _0$ ($\approx 10^{4}$ S.m$^{-1}$) in the investigated spectral range (see Eq. (1)). Quantum corrections would be more important if the junction was composed only of metals as in the work of Esteban et al. [33] or by a small band gap semiconductor with a higher electrical conductivity.

 

Fig. 4. Average electric near-field enhancements for a tunneling junction excited by (A) a p- and (B) s-polarized incident light calculated without (dashed lines) and with (continuous lines) QCM correction. The tip-surface distance is $l=0.2$ nm and the bias voltage is $V=2$ V.

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For s-polarization (Fig. 4(B)), the presence of the effective medium in the tip-surface gap region and the resulting quantum corrections do not affect the Fano-lineshape interference of the plasmon-exciton resonances because the corresponding electric near-field is localized mainly at the $MoSe_2/Au$ interface (see Fig. 3(D)) away from the effective medium which accounts for tunneling.

3.3 Tuning of gap plasmon modes

In this section, we focus on gap plasmon resonances excited with p-polarized light and their dependencies on tip-surface distance and bias voltage. For gap distances in the tunneling regime ($l< 0.5$ nm), we use QCM-DDA simulations. We compute the maximum electric near-field enhancement inside a volume which includes the gap, the tip apex and part of the $MoSe_2$ layer. The electric field enhancement in the gap region depends on the geometric volume of the plasmonic cavity [41,46]. Therefore, in order to compute the near-field intensity, we calculate the maximum electric field enhancement instead of averaging it over a given volume.

The maximum electric field enhancement is computed : (i) by varying the tip-surface distance $l$ from $l=0.2$ nm to $l=2$ nm, QCM-DDA simulations are performed for $l=0.2,\,0.3,\,0.4$ nm and $V=2$ V, (ii) by varying the bias voltage $V$ from $V=1.5$ V to $V=2.25$ V and keeping the tip-surface distance constant $l=0.2$ nm (QCM-DDA).

As shown in Fig. 5(A), when the tip-surface distance decreases, the gap plasmon resonance strongly redshifts and its intensity increases because of the Coulomb interaction between the polarization charges accumulated at the opposite sides of the gap. In the tunneling regime $l < 0.5$ nm, the gap plasmon resonance redshift is even more pronounced because of the tunneling conductivity of the effective medium introduced in the gap region (Eq. (1)).

 

Fig. 5. Maximum electric near-field enhancement calculated inside the gap region between the tip apex and the $MoSe_2$ layer for p-polarized incident light. (A) For tip-surface distances $l$ ranging from $l=0.2$ nm to $l=2$ nm. The QCM is used with a bias voltage of $V=2$ V for tip-surface distances $l < 0.5$ nm. (B) For bias voltages $V$ ranging from $V=1.5$ V to $V=2.25$ V and $l=0.2$ nm; the QCM is used.

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Figure 5(B) shows the dependence of the gap plasmon resonance on bias voltage $V$. No significant difference among the calculated spectra is obtained. For $V$ ranging from $1.5$ V to $2.25$ V, and a tip-surface distance set to $l=0.2$ nm, $\sigma (l,V)$ increases by nearly a factor of $24$, from $0.168$ S.m$^{-1}$ to $4.01$ S.m$^{-1}$, but these values are still very small compared to $\omega \epsilon _0$ (Eq. (1)) and therefore, the variation of bias voltage does not affect the gap plasmon resonance.

3.4 Plasmon-exciton coupling

In this section, we investigate the Fano-type plasmon-exciton coupling in the far-field. From DDA calculations, we compute the far-field extinction spectra and we analyze their spectral lineshape using a two coupled-oscillator analytical model. The extinction cross-section $C_{ext}(\omega )$ can be written as [28,29,48]:

where $\omega _{ex}$ and $\gamma _{ex}$ are the angular frequency and damping parameter of the A-exciton respectively; $\omega _{sp}$ and $\gamma _{sp}$ are the angular frequency and damping parameter of the surface plasmon mode, respectively. $\hbar g$ corresponds to the interaction energy between the two oscillators. We assume that the properties of the excitons confined within the $MoSe_2$ monolayer are independent of the tunneling parameters $l$ and $V$. Throughout the fitting procedure, the values of $\hbar \omega _{ex}$ and $\hbar \gamma _{ex}$ are kept constant: $\hbar \omega _{ex}=1.56$ eV and $\hbar \gamma _{ex}=42$ meV [29]. Since the surface plasmon modes are very sensitive to the presence of the $MoSe_2$ monolayer in the junction and to the tunneling parameters, $\hbar \omega _{sp}$, $\hbar \gamma _{sp}$ and $\hbar g$ are adjustable parameters.

The far-field extinction spectra have been computed using DDA for s and p-polarizations (black lines in Fig. 6) and fitted using Eq. (3) (red lines in Fig. 6) for tip-surface distances ranging from $l=0.2$ nm to $l=2$ nm.

 

Fig. 6. Evolution of the plasmon-exciton coupling strength as a function of the tip-surface distance $l$ for p- (A) and s- (B) polarized light. For distances $l<0.5$ nm (tunneling regime), the QCM is used with a bias voltage of $V=2$ V. (A-B) Optical extinction spectra of our hybrid system obtained for different tip-surface distances $l$. Black lines: DDA calculated spectra of far-field optical extinction cross-section (in units of $\pi a^{2}$, $a$ being the radius of the sphere of equivalent volume). Red lines: spectra calculated using the coupled-oscillator model and fitted to the DDA spectra. (C) Tip-surface distance $l$ dependence of the plasmon-exciton coupling strength $\hbar g$ obtained from the fitting procedure for p- and s-polarizations.

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First, one can notice that for s-polarization, the Fano-dip is more pronounced than for p-polarization independently of the tip-surface distance as shown in Fig. 6(A-B). Indeed, a stronger plasmon-exciton coupling takes place when the junction is excited by an s-polarized light because of the stronger localization of the plasmonic near-field within the $MoSe_2$ layer. Moreover, for s-polarization, we obtain $\hbar g=47.8\,\pm \,1.50$ meV regardless of the tip-surface distance since the plasmon-exciton coupling is mainly localized at the $MoSe_2/Au$ interface and is therefore not sensitive to the tip-surface distance.

For p-polarization, $\hbar g$ increases from $44.5\,\pm \,1.60$ meV for $l=0.2$ nm to $\hbar g=47.3\,\pm \,1.50$ meV for $l=2$ nm.

The near-field spectra obtained for p-polarization (see Fig. 5(A)) show that the gap plasmon resonance is highly dependent on the tip-surface distance. This dependence is reflected in the far-field by the diminution of the plasmon-exciton coupling with decreasing tip-surface distance. Indeed, in Fig. 7, we observe that the electric field of the gap plasmon mode (excited in p-polarization) tends to localize in the gap region for $l<1$ nm. As a consequence, overlapping with the $MoSe_2$ layer where the excitons are confined decreases (Fig. 7(A-B)) leading to smaller plasmon-exciton coupling with decreasing tip-surface distance. Notice that for $l=2$ nm, the plasmon-exciton mode with a maximum enhancement at the $MoSe_2$/$Au$ interface is now clearly visible in p-polarization (Fig. 7(B)). For $l\ge 2$ nm, $\hbar g\approx 47.5$ meV for both s and p-polarizations since the plasmon-exciton field is excited by the incident polarization component parallel to the layer.

 

Fig. 7. Electric near-field enhancement maps (in log scale) of the $Au$/$MoSe_2$/$Au$ junction calculated in the yz plane for a tip-surface distance (A) of $l=0.2$ nm and (B) of $l=2$ nm. In both cases, the simulated junction is illuminated by a p-polarized incident light at $\lambda =800$ nm. QCM is used for $l=0.2$ nm with a bias voltage of $V=2 V$

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In order to confirm the Fano-type coupling, we define the critical value $\hbar g_c=(\hbar \gamma _{ex}+\hbar \gamma _{sp})/2$. In our case, $\hbar \gamma _{sp}$ $\approx 185$ meV is determined from the fitting procedure (see Tables S1 and S2 in Supplement 1). The A-exciton damping is $\hbar \gamma _{ex}=42$ meV and hence, $\hbar g_c$ is around $\approx 113$ meV. The values of $\hbar g$ (around $47$ meV) obtained from the fitting procedure (see Fig. 6) are around $2.4$ times smaller than $\hbar g_c$ which confirms the Fano-type coupling regime.

Finally, the dependence of the coupling strength $\hbar g$ on bias voltage $V$ is investigated (see Fig.S5 in Supplement 1). For $V$ ranging from $1.5$ V to $2.25$ V, the permittivity of the effective media does not change significantly as discussed above. In addition, the plasmon-exciton coupling is localized at the $MoSe_2/Au$ interface and therefore does not depend on the effective medium tunneling conductivity.

In DDA simulations, the target object has a finite size. Therefore, the surface plasmon resonances of the tip and the substrate depend on the shape of the tip and the dimensions of the substrate. In our case, the later were chosen in such a way that tip and substrate resonances do match the $MoSe_2$ exciton resonance. In the supplemental document are shown the DDA far-field spectra calculated for various tip lengths (Fig. S6 in Supplement 1) and various substrate dimensions (Fig. S7 in Supplement 1) and tuning/detuning resonance conditions with respect to the $MoSe_2$ excitonic resonance. In actual systems, the coherence length of plasmon-polaritons is limited by disorder effects due to surface roughness and polycrystalline gold. As a result, rather than plasmon-polaritons reflected back and forth on the tip and the substrate boundaries, the plasmonic resonances should be considered as spectrally distributed local surface plasmon resonances which tend to hybridize, because of the near-field interaction between the tip and the substrate, thus forming gap-plasmons. Close to the $MoSe_2$ exciton wavelength, such resonances may also form hybrid plasmon-exciton modes. In actual systems, the plasmon resonances involved in STM experiments, may be different from the tip and substrate resonances addressed in this work, but the physics governing how gap plasmons might emerge and interact with TMD layers can be captured with the simple modeling here presented, without loss of generality. A step forward towards a more realistic modeling would be to include tip and surface roughness to allow for local surface plasmon resonances.

4. Conclusion

In this work, we have reported a theoretical investigation of the plasmon-exciton coupling in a hybrid metal/semiconductor nano-junction formed by a $MoSe_2$ monolayer supported by a Au substrate and the tip of a scanning tunneling microscope. The optical response of this hybrid junction to an incident optical excitation allows to identify its electromagnetic eigenmodes and their dependence on the incident polarization and the tunneling parameters, i.e. tip-surface distance and bias voltage. Quantum corrections have been introduced in the DDA numerical simulations to take into account electron tunneling. We have shown that these quantum corrections as well as the anisotropic character of the $MoSe_2$ layer do not have a significant impact on the electromagnetic modes of the hybrid $Au/MoSe_2/Au$ junction in the non-contact regime ($l\ge 0.2$ nm). Our main findings can be summarized as follows: (i) a Fano-type coupling between the localized surface plasmon modes of the tunneling junction and the excitons confined in the $MoSe_2$ layer is observed in the far and near-field. This coupling takes place at the interface between the $MoSe_2$ layer and the substrate giving rise to a hybrid interface plasmon-exciton mode. Using a coupled oscillators model, a plasmon-exciton interaction energy of $\hbar g=47.8\,\pm \,1.50$ meV is obtained. (ii) When the polarization is along the tip axis, gap plasmon modes are excited and their spectral properties and spatial localization are tuned by the tip-surface distance. (iii) The plasmon-exciton interaction strength can be tuned by tunneling distance. When gap plasmon modes are excited, the plasmonic field is more localized in the gap region than at the $MoSe_2/Au$ interface leading to a lowering of the plasmon-exciton interaction. The results presented in this work pave the way towards a better understanding of the complex light-matter interaction between localized surface plasmons and excitons in an STM configuration. The presented work provides a good starting point to carry out a theoretical model of the STM-induced excitonic luminescence from TMD. In future work, it would be interesting to take into account the inelastic tunneling by considering a point-like oscillating electric dipole as the excitation source.