Scanning Near-Field Optical Microscopy of Ultrathin Gold Films

Ultrathin metal films are an essential platform for two-dimensional (2D) material compatible and flexible optoelectronics. Characterization of thin and ultrathin film-based devices requires a thorough consideration of the crystalline structure and local optical and electrical properties of the metal-2D material interface since they could be dramatically different from the bulk material. Recently, it was demonstrated that the growth of gold on the chemical vapor deposited monolayer MoS2 leads to a continuous metal film that preserves plasmonic optical response and conductivity even at thicknesses below 10 nm. Here, we examined the optical response and morphology of ultrathin gold films deposited on exfoliated MoS2 crystal flakes on the SiO2/Si substrate via scattering-type scanning near-field optical microscopy (s-SNOM). We demonstrate a direct relationship between the ability of thin film to support guided surface plasmon polaritons (SPP) and the s-SNOM signal intensity with a very high spatial resolution. Using this relationship, we observed the evolution of the structure of gold films grown on SiO2 and MoS2 with an increase in thickness. The continuous morphology and superior ability with respect to supporting SPPs of the ultrathin (≤10 nm) gold on MoS2 is further confirmed with scanning electron microscopy and direct observation of SPP fringes via s-SNOM. Our results establish s-SNOM as a tool for testing plasmonic films and motivate further theoretical research on the impact of the interplay between the guided modes and the local optical properties on the s-SNOM signal.


Introduction
Ultrathin metal films are essential elements of novel optoelectronic, photonic, and plasmonic devices [1][2][3]. Thanks to their transparency, conductivity, and mechanical stability, gold, silver, or copper ultrathin films of thicknesses below 10 nm are a promising platform for developing flexible transparent electrodes in various optoelectronic applications [4,5]. For example, plasmonic waveguides, hyperbolic metamaterials, and transparent electrodes made from ultrathin films should possess smooth and continuous structural morphology to have a superior optical response and electronic properties [6][7][8]. To realize ultrathin film growth, the conventional three-dimensional (3D) mechanism in the Volmer-Weber regime [9] should be avoided by using special deposition conditions [10] or inserting additional wetting layers [11]. One of the competing methods to obtain continuous two-dimensional (2D) metal growth on a substrate is employing atomically thin two-dimensional (2D) underlayers, such as monolayer or few-layer graphene or transition metal dichalcogenide (TMD), which favors continuous metal growth kinetics [12][13][14]. Among them, molybdenum disulfide (MoS 2 ) has received large attention due to its tunable bandgap, high refractive index, and giant optical anisotropy resulting in a wide range of applications from field-effect transistors to solar cells and photodetectors [15][16][17][18][19]. In this regard, investigation of Au/MoS 2 or other TMD interfaces is of great practical interest.
Recently, 2D MoS 2 layers demonstrated impressive results of gold ultrathin film growth. Due to the surface wetting effect and the adhesion of gold to MoS 2 , high nucleation density and unusual kinetics of Au adatoms on MoS 2 surface lead to the growth of continuous and ultrasmooth clusters and highly-percolated structures [13,[20][21][22]. In recent papers, a detailed investigation of metal growth on MoS 2 revealed the formation of atomically flat Au clusters, nanotriangles, and nanoparticles depending on the deposition technique, metal thickness, and temperature [20,21,[23][24][25][26][27]. For example, the presence of MoS 2 could enhance the performance of ultrathin noble metal electrodes and their optical response [22,25,[28][29][30]. At the same time, the decoration of 2D MoS 2 layers with nanoparticles helps to control and improve the characteristics of transistors, photodetectors, and Raman sensors [23,31,32]. However, despite its great importance, there is still no detailed study of continuous ultrathin gold films grown on exfoliated MoS 2 .
Investigation of the optical response of continuous gold films grown on small (~1 µm) flakes of MoS 2 and nanoscale structures via far-field optical techniques, such as spectroscopic ellipsometry and reflectometry, is challenging. Nevertheless, one can study the optical properties on the nanometer scale via scanning optical probe methods. Among them, s-SNOM is a powerful technique for probing the optical response in material with nanoscale resolution [33]. In particular, s-SNOM was successfully utilized for the characterization of thin films [34], nanoparticles [35,36], optoelectronic devices [37], surface enhanced Raman spectroscopy biosensors [38,39] and layered van der Waals materials, such as graphene and TMDs [40][41][42]. Furthermore, in plasmonics and photonics, s-SNOM is an effective tool for the excitation and detection of surface plasmon and phonon polaritons in layered structures [43]. The detected s-SNOM signal strongly depends on the optical response of the tip-sample interaction area, which governs the scattering efficiency of light by the tip [44,45]. As a result, the light scattering efficiency by the tip in the near-field is stronger on metal with a higher modulus of the real part of permittivity [46,47]. In practice, this results in a high contrast in s-SNOM amplitude and phase between the metal and dielectric areas of the sample, which are distinguishable with nanoscale spatial resolution [45,46]. This fact allows to perform mapping of the local homogeneity of dielectric permittivity of the material, analyze the quality of the sample morphology, and identify sub-diffraction features on the surface [45,48,49]. Our previous work demonstrated that, for ultrathin gold films grown on different 2D materials, the s-SNOM near-field intensity correlates well with their far-field dielectric response [50].
This study demonstrates the transformation of gold film morphology during growth on exfoliated MoS 2 flakes. Furthermore, morphological study with scanning electron and atomic-force microscopies was extended with s-SNOM near-field studies, which allowed to demonstrate of a qualitative improvement of plasmonic properties and structural evolution of metallic films on MoS 2 , which is crucial for next-generation ultrathin metal optoelectronics.

Materials and Methods
For the deposition of gold films, MoS 2 2D-crystal flakes were prepared via mechanical exfoliation on SiO 2 /Si wafer using scotch tape and bulk MoS 2 crystal (2D semiconductors). To remove scotch residuals, the exfoliated flakes with substrates were carefully cleaned in acetone prior to deposition. Then, gold films were deposited via the electron-beam evaporation method in a high vacuum (~10 −6 Torr) chamber setup (Nano-Master NEE-4000, Austin, TX, USA) at room temperature onto the prepared substrate of MoS 2 flakes/SiO 2 . The mass-equivalent thicknesses of gold in the range of 4-10 nm and the deposition rate of 1 A/s were measured in-situ via a calibrated quartz-crystal sensor. The crystal quality of MoS 2 flakes and the number of atomic layers in them were assessed by confocal Raman microscope Horiba LabRAM HR Evolution (Horiba Ltd., Kyoto, Japan). All measurements were carried out with laser excitation wavelengths of The structural morphology of the deposited Au films was visualized via scanning electron microscopy (SEM, JSM7001F, JEOL, Tokyo, Japan) working in the secondary electron imaging mode with a Schottky emitter, an acceleration voltage of 30 kV and a working distance of~6 mm. To characterize the surface roughness and homogeneity of films, we performed atomic force microscopy (AFM, Ntegra II, NT-MDT Spectrum Instruments, Moscow, Russia) working in the peak-force mode with a tip of radius <10 nm and a resonant cantilever frequency of~140 kHz (NT-MDT, ETALON, HA_NC).
Optical near-field characterization of Au films grown on MoS 2 flakes was performed using a scattering-type scanning near-field optical microscope (s-SNOM, neaSNOM, Neaspec GmbH, Haar, Germany) working in the reflection mode [46,47]. In this setup, we used a standard AFM tip coated with platinum, working in the tapping mode with a resonance frequency of Ω ≈ 280 kHz. The s-SNOM tip was illuminated via a focused linearly polarized laser beam (λ = 1550 nm) with an angle to the sample surface of about 50 • . Next, the near-field was scattered by the tip interacting with the surface and redirected by an upper parabolic mirror to a highly sensitive photodetector. In addition, a pseudo-heterodyne interferometric scheme and demodulation of the detected scattered signal at higher harmonics (4 Ω) were used for acquiring a near-field signal filtered from the background contribution.

Results and Discussion
First, few-layered MoS 2 flakes were located on the SiO 2 (285 nm)/Si substrate by their color contrast using an optical microscope. A typical optical image of the prepared flake with terraces consisting of a few MoS 2 layers is shown in Figure 1a. The crystal quality and the number of layers were determined via Raman spectroscopy of the different areas marked with white dots in Figure 1a. The obtained Raman spectra exhibited typical MoS 2 peaks E 1 2g (~384 cm −1 ) and A 1g (~407 cm −1 ). The observed broadening and shifts of the distance between E 1 2g and A 1g Raman modes in the spectra in Figure 1b indicated an increase in MoS 2 thickness, consistent with the previously reported results [51]. The crystal quality of MoS2 flakes and the number of atomic layers in them were assessed by confocal Raman microscope Horiba LabRAM HR Evolution (Horiba Ltd., Kyoto, Japan). All measurements were carried out with laser excitation wavelengths of 632.8 nm with an 1800 lines/mm diffraction grating and a ×100 (N.A. = 0.90) objective. The spot diameter was ~0.5 μm.
The structural morphology of the deposited Au films was visualized via scanning electron microscopy (SEM, JSM7001F, JEOL, Tokyo, Japan) working in the secondary electron imaging mode with a Schottky emitter, an acceleration voltage of 30 kV and a working distance of ~6 mm. To characterize the surface roughness and homogeneity of films, we performed atomic force microscopy (AFM, Ntegra II, NT-MDT Spectrum Instruments, Moscow, Russia) working in the peak-force mode with a tip of radius <10 nm and a resonant cantilever frequency of ~140 kHz (NT-MDT, ETALON, HA_NC).
Optical near-field characterization of Au films grown on MoS2 flakes was performed using a scattering-type scanning near-field optical microscope (s-SNOM, neaSNOM, Neaspec GmbH, Haar, Germany) working in the reflection mode [46,47]. In this setup, we used a standard AFM tip coated with platinum, working in the tapping mode with a resonance frequency of Ω ≈ 280 kHz. The s-SNOM tip was illuminated via a focused linearly polarized laser beam (λ = 1550 nm) with an angle to the sample surface of about 50°. Next, the near-field was scattered by the tip interacting with the surface and redirected by an upper parabolic mirror to a highly sensitive photodetector. In addition, a pseudo-heterodyne interferometric scheme and demodulation of the detected scattered signal at higher harmonics (4 Ω) were used for acquiring a near-field signal filtered from the background contribution.

Results and Discussion
First, few-layered MoS2 flakes were located on the SiO2 (285 nm)/Si substrate by their color contrast using an optical microscope. A typical optical image of the prepared flake with terraces consisting of a few MoS2 layers is shown in Figure 1a. The crystal quality and the number of layers were determined via Raman spectroscopy of the different areas marked with white dots in Figure 1a. The obtained Raman spectra exhibited typical MoS2 peaks E 1 2g (~384 cm −1 ) and A1g (~407 cm −1 ). The observed broadening and shifts of the distance between E 1 2g and A1g Raman modes in the spectra in Figure 1b indicated an increase in MoS2 thickness, consistent with the previously reported results [51]. To demonstrate the drastic difference in the morphology of Au film on MoS2 and SiO2 underlayers, a SEM image of the boundary between Au/MoS2 and Au/SiO2 was recorded (see Figure 1c and Figure A1). Clearly, ultrathin gold films on MoS2 are continuous and To demonstrate the drastic difference in the morphology of Au film on MoS 2 and SiO 2 underlayers, a SEM image of the boundary between Au/MoS 2 and Au/SiO 2 was recorded (see Figures 1c and A1). Clearly, ultrathin gold films on MoS 2 are continuous and without voids, while ultrathin gold films on SiO 2 are composed of particles separated by voids. A similar difference in the morphology of gold on MoS 2 and SiO 2 was previously observed for gold films on MoS 2 monolayers grown by chemical vapor deposition (CVD) [22]. As can be seen, microscopy images show no visible variation in the morphology of Au grown on the different terraces of MoS 2 .
After the metal deposition, the surface morphology of the Au films grown on few-layer MoS 2 was further examined via SEM and AFM. As seen in Figure 2, both the SEM (a-c) and AFM (d-f) images indicate that 4-10-nm-thick Au films on few-layer MoS 2 fully cover the substrate. The polycrystalline structure of Au films was confirmed via SEM images as in Figure 2a-c. The full area metal coverage is due to a low percolation threshold and high density of nucleation sites at the initial stage of the film growth on MoS 2 . AFM surface analysis demonstrated in Figure 2d-f revealed an atomically smooth surface with a root-mean-square (RMS) roughness below 0.37 nm for all considered thicknesses, which additionally confirms full substrate coverage by the gold film. At the same time, surface roughness slightly increases with the increase in gold layer thickness, which is typical for continuous polycrystalline Au films [52,53]. without voids, while ultrathin gold films on SiO2 are composed of particles separa voids. A similar difference in the morphology of gold on MoS2 and SiO2 was prev observed for gold films on MoS2 monolayers grown by chemical vapor deposition [22]. As can be seen, microscopy images show no visible variation in the morphol Au grown on the different terraces of MoS2.
After the metal deposition, the surface morphology of the Au films grown o layer MoS2 was further examined via SEM and AFM. As seen in Figure 2, both th (a-c) and AFM (d-f) images indicate that 4-10-nm-thick Au films on few-layer MoS cover the substrate. The polycrystalline structure of Au films was confirmed via SE ages as in Figure 2a-c. The full area metal coverage is due to a low percolation thr and high density of nucleation sites at the initial stage of the film growth on MoS2 surface analysis demonstrated in Figure 2d-f revealed an atomically smooth surfac a root-mean-square (RMS) roughness below 0.37 nm for all considered thicknesses, additionally confirms full substrate coverage by the gold film. At the same time, s roughness slightly increases with the increase in gold layer thickness, which is typ continuous polycrystalline Au films [52,53]. To probe the local optical response of gold films, we performed s-SNOM micro For the measurements, we chose areas that include the boundary between Au/SiO Au/MoS2 which allowed us to visualize the contrast between the optical properties ferent gold films. Moreover, we focused on monolayer MoS2 underlayers rather tha tilayer MoS2 to minimize the influence of MoS2 on the s-SNOM amplitude. The s-S scans of the boundary between Au/MoS2 and Au/SiO2 for Au layer thicknesses of 4 10 nm are demonstrated in Figure 3a-c. Here, the near-field amplitude showed contrast between Au films grown on the MoS2 and SiO2 surface for all thicknesses, w s-SNOM amplitude at the area of Au/MoS2 being significantly higher than that for d tinuous film Au/SiO2. Furthermore, the contrast between Au/MoS2 and Au/SiO2 with the increase in the gold thickness, starting from about 50% for 4-nm-thick film ure 3a) to an order of magnitude for 10-nm-thick films (Figure 3c).
Higher quality of Au/MoS2 films on CVD MoS2 was previously established by t field measurements [22] and is qualitatively evident from Figure 1c. Nevertheless, additional confirmation we analyzed topography scans presented in Figure 3d clearly see the existence of a 3-5-nm-high step on the boundary between Au/SiO Au/MoS2, in agreement with the previous AFM measurements [20]. Such a differe To probe the local optical response of gold films, we performed s-SNOM microscopy. For the measurements, we chose areas that include the boundary between Au/SiO 2 and Au/MoS 2 which allowed us to visualize the contrast between the optical properties of different gold films. Moreover, we focused on monolayer MoS 2 underlayers rather than multilayer MoS 2 to minimize the influence of MoS 2 on the s-SNOM amplitude. The s-SNOM scans of the boundary between Au/MoS 2 and Au/SiO 2 for Au layer thicknesses of 4, 7 and 10 nm are demonstrated in Figure 3a-c. Here, the near-field amplitude showed a high contrast between Au films grown on the MoS 2 and SiO 2 surface for all thicknesses, with an s-SNOM amplitude at the area of Au/MoS 2 being significantly higher than that for discontinuous film Au/SiO 2 . Furthermore, the contrast between Au/MoS 2 and Au/SiO 2 grows with the increase in the gold thickness, starting from about 50% for 4-nm-thick films (Figure 3a) to an order of magnitude for 10-nm-thick films (Figure 3c). between the topography and amplitude maps; for example, some bright spots on the left side of Figure 3d,e turn into dark spots in Figure 3a,b. Moreover, the fluctuation of the near-field amplitude of Au/MoS2 films grows from 16.8⋅10 −3 to 21.5⋅10 −3 as their thickness increases. Similar behavior is observed for topography scans that show the increase in the surface roughness of Au/MoS2 from 0.29 to 0.37 nm (Figure 2d-f). These results suggest that the near-field amplitude represents the local optical properties and morphology of gold films, in the spirit of the seminal work [45]. Apart from local optical response distribution, s-SNOM could give additional information about ultrathin film properties as a whole. Indeed, the s-SNOM signal on the surface of the metal depends not only on the scattering properties of the SNOM tip and a sample area immediately underneath it but also on the guided SPP waves that can be excited by the tip and propagate up to dozens of micrometers along the film. The excitation of guided SPP is detectable via near-field fringes typically visible near the line cracks and other defects. Interestingly, despite the straight-line boundary between Au/MoS2 and Au/SiO2, no interference fringes are visible in Figure 3a,b. By contrast, a large 10 × 10 μm 2 area scan of 10-nm-thick Au/MoS2 film reveals a line defect and a fringe pattern around it (see Figure 4a). These fringes clearly indicate the capability of the Au/MoS2 film to guide SPP waves. At the same time, the absence of fringes in Figure 3a-c can be related to the porous nature of Au/SiO2 film. Below the percolation threshold, the propagation of SPP waves can occur due to the dipole-dipole coupling between adjacent metallic islands, while above the percolation threshold the SPP wave is scattered by the disordered voids in the metal film. As a result, in both cases the phase coherence of SPP waves is rapidly lost, which, combined with the local fluctuations of optical properties, produces noisy amplitude maps in Figure 3a  Higher quality of Au/MoS 2 films on CVD MoS 2 was previously established by the far-field measurements [22] and is qualitatively evident from Figure 1c. Nevertheless, for the additional confirmation we analyzed topography scans presented in Figure 3d-f. We clearly see the existence of a 3-5-nm-high step on the boundary between Au/SiO 2 and Au/MoS 2 , in agreement with the previous AFM measurements [20]. Such a difference in thickness can be explained by the higher porosity of Au/SiO 2 films which makes the total volume of Au/SiO 2 film higher than that of Au/MoS 2 film despite the same quantity of metal per unit area being deposited on each substrate. Interestingly, there are correlations between the topography and amplitude maps; for example, some bright spots on the left side of Figure 3d,e turn into dark spots in Figure 3a,b. Moreover, the fluctuation of the near-field amplitude of Au/MoS 2 films grows from 16.8·10 −3 to 21.5·10 −3 as their thickness increases. Similar behavior is observed for topography scans that show the increase in the surface roughness of Au/MoS 2 from 0.29 to 0.37 nm (Figure 2d-f). These results suggest that the near-field amplitude represents the local optical properties and morphology of gold films, in the spirit of the seminal work [45].
Apart from local optical response distribution, s-SNOM could give additional information about ultrathin film properties as a whole. Indeed, the s-SNOM signal on the surface of the metal depends not only on the scattering properties of the SNOM tip and a sample area immediately underneath it but also on the guided SPP waves that can be excited by the tip and propagate up to dozens of micrometers along the film. The excitation of guided SPP is detectable via near-field fringes typically visible near the line cracks and other defects. Interestingly, despite the straight-line boundary between Au/MoS 2 and Au/SiO 2 , no interference fringes are visible in Figure 3a,b. By contrast, a large 10 × 10 µm 2 area scan of 10-nm-thick Au/MoS 2 film reveals a line defect and a fringe pattern around it (see Figure 4a). These fringes clearly indicate the capability of the Au/MoS 2 film to guide SPP waves. At the same time, the absence of fringes in Figure 3a-c can be related to the porous nature of Au/SiO 2 film. Below the percolation threshold, the propagation of SPP waves can occur due to the dipole-dipole coupling between adjacent metallic islands, while above the percolation threshold the SPP wave is scattered by the disordered voids in the metal film. As a result, in both cases the phase coherence of SPP waves is rapidly lost, Next, using the capabilities of our s-SNOM setup to measure both the amplitude and phase of the near-field signal, we analyze them to retrieve an effective-mode index of propagation of surface plasmon modes. We carried out a one-dimensional complex Fourier transformation (FT) of the averaged s-SNOM signal along the SPP propagation, as illustrated in Figure 4a by the arrow, which allowed us to extract effective mode indices. As indicated in Figure 4c (the red arrows), the Fourier spectrum has three peaks k/k0 ≈ 1.87, 2.56 and −0.85; due to the geometry of the reflection mode s-SNOM setup, the "real" values k/k0 of the modes are shifted from the k/k0 observable in the experiment [54]. The value of the shift can be expressed as: β0 = kR + k0·cos α·sin β β0/k0 = kR/k0 + cos α·sin β, β0 = kL − k0·cos α·sin β β0/k0 = kL/k0 -cos α·sin β, where β0 corresponds to the observable mode, kR/k0 stays for the "real" effective mode index for the modes on the right side of the Fourier transform, kL/k0-for the left side, α is the angle between the wave vector of the incident light and its projection on the sample surface and β is the angle between the projection of the wave vector and the crack from which the light scatters. In our case, the shift is 0.86 due to the geometry of the experimental setup. According to Equations (1) and (2), we observe two propagating modes in the Fourier spectrum: one with effective-mode index 1.71 (β0/k0 ≈ 2.56 and β0/k0 ≈ −0.85) and the other with 1.02 (β0/k0 ≈ 1.87). The latter propagates along the air/Au interface (k/k0 ≈ 1.02) while the former along the interface between Au and the substrate (k/k0 ≈ 1.71).
In addition, we verified experimental effective-mode indexes by finding the film dielectric constants ε′ and ε″ via comparison of experimentally determined neff with theoretically calculated neff t . For this, we performed full-wave electromagnetic simulations using COMSOL Multiphysics to obtain neff t selecting different values of dielectric functions ε′ and ε″ of 10-nm-thick gold film at a single wavelength of λ = 1550 nm. Results of the calculated difference neff t − neff are presented in Figure 4d. Here, the darker the color of the map, the closer the modes that are obtained for the ε′ and ε″ data are to the effective mode indices that are observed in the experiment. It is seen that the effective mode index mainly depends on ε′. At the same time, ε″ is responsible for propagation losses, which are difficult to determine from s-SNOM map, thus can be varied within a reasonable range. From Figure 4d, the ranges for the dielectric function of gold are |ε′| = 90-92.5, ε″ = 10-20 (darkest areas in Figure 4d indicated by the white dotted line) which is in agreement with the formerly measured dielectric constants ε′ = −95.3 and ε″ = 14.5 at λ = 1550 nm of 9-nmthick gold film grown on MoS2-CVD monolayer [22]. To sum up, the high quality of Au/MoS2 films was demonstrated by s-SNOM image contrast measurements in Figure 3c, SEM in Figure 2, and by the observation of SPP fringes in Figure 4a. Also, we determined Next, using the capabilities of our s-SNOM setup to measure both the amplitude and phase of the near-field signal, we analyze them to retrieve an effective-mode index of propagation of surface plasmon modes. We carried out a one-dimensional complex Fourier transformation (FT) of the averaged s-SNOM signal along the SPP propagation, as illustrated in Figure 4a by the arrow, which allowed us to extract effective mode indices. As indicated in Figure 4c (the red arrows), the Fourier spectrum has three peaks k/k 0 ≈ 1.87, 2.56 and −0.85; due to the geometry of the reflection mode s-SNOM setup, the "real" values k/k 0 of the modes are shifted from the k/k 0 observable in the experiment [54]. The value of the shift can be expressed as: where β 0 corresponds to the observable mode, k R /k 0 stays for the "real" effective mode index for the modes on the right side of the Fourier transform, k L /k 0 -for the left side, α is the angle between the wave vector of the incident light and its projection on the sample surface and β is the angle between the projection of the wave vector and the crack from which the light scatters. In our case, the shift is 0.86 due to the geometry of the experimental setup. According to Equations (1) and (2), we observe two propagating modes in the Fourier spectrum: one with effective-mode index 1.71 (β 0 /k 0 ≈ 2.56 and β 0 /k 0 ≈ −0.85) and the other with 1.02 (β 0 /k 0 ≈ 1.87). The latter propagates along the air/Au interface (k/k 0 ≈ 1.02) while the former along the interface between Au and the substrate (k/k 0 ≈ 1.71).
In addition, we verified experimental effective-mode indexes by finding the film dielectric constants ε and ε" via comparison of experimentally determined n eff with theoretically calculated n eff t . For this, we performed full-wave electromagnetic simulations using COMSOL Multiphysics to obtain n eff t selecting different values of dielectric functions ε and ε" of 10-nm-thick gold film at a single wavelength of λ = 1550 nm. Results of the calculated difference n eff t − n eff are presented in Figure 4d. Here, the darker the color of the map, the closer the modes that are obtained for the ε and ε" data are to the effective mode indices that are observed in the experiment. It is seen that the effective mode index mainly depends on ε . At the same time, ε" is responsible for propagation losses, which are difficult to determine from s-SNOM map, thus can be varied within a reasonable range. From Figure 4d, the ranges for the dielectric function of gold are |ε | = 90-92.5, ε" = 10-20 (darkest areas in Figure 4d indicated by the white dotted line) which is in agreement with the formerly measured dielectric constants ε = −95.3 and ε" = 14.5 at λ = 1550 nm of 9-nm-thick gold film grown on MoS 2 -CVD monolayer [22]. To sum up, the high quality of Au/MoS 2 films was demonstrated by s-SNOM image contrast measurements in Figure 3c, SEM in Figure 2, and by the observation of SPP fringes in Figure 4a. Also, we determined the effective index of SPPs propagating along the 10-nmthick gold film, and, based on it, extracted the effective values of ε and ε" of the gold film, which agree with the previous measurements.

Conclusions
We studied morphology and local optical response of ultrathin gold films deposited on SiO 2 and 2D MoS 2 crystal layers. The results demonstrate the significant contrast in s-SNOM amplitude between Au films on MoS 2 and SiO 2 for all measured thicknesses. As was observed, strong contrast in the s-SNOM signal is related to the different surface morphology and continuity of Au films deposited on SiO 2 and MoS 2 surfaces, which correlates well with the previously reported far-field and near-field investigations. Furthermore, we detected SPP wave propagation at the telecom wavelength range via s-SNOM imaging of near-field fringes from edge defect in 10-nm-thick Au film on MoS 2 , and theoretically calculated possible dielectric permittivities of gold. The observation of SPP propagation additionally confirms the high quality of the obtained ultrathin films. As a result, by obtaining nanoscale optical images, we demonstrated s-SNOM to be an effective method for analysis of the structural quality and optical response, which can give information about the propagation of surface waves in ultrathin metal films. We believe that our research will encourage the future use and deep theoretical study of s-SNOM for advanced nanoscale optical characterization of the optical and structural performance of metal-2D material interfaces. Figure A1. The comparison SEM images for gold films grown on SiO 2 and MoS 2 for 4 nm, 7 nm, and 10 nm film thickness.