Improving resolution in quantum subnanometre-gap tip-enhanced Raman nanoimaging

Two-dimensional (2D) materials beyond graphene such as transition metal dichalcogenides (TMDs) have unique mechanical, optical and electronic properties with promising applications in flexible devices, catalysis and sensing. Optical imaging of TMDs using photoluminescence and Raman spectroscopy can reveal the effects of structure, strain, doping, edge states, and surface functionalization from materials to bioscience. However, Raman signals are inherently weak and so far have been limited in spatial resolution in TMDs to a few hundred nanometres which is much larger than the intrinsic scale of these effects. Here we overcome the diffraction limit by using resonant tip-enhanced Raman scattering (TERS) of few-layer MoS2, and obtain nanoscale optical images with ~20 nm spatial resolution. This becomes possible due to electric field enhancement in an optimized subnanometre-gap resonant tip-substrate configuration. We investigate the limits of signal enhancement by varying the tip-sample gap with sub-Angstrom precision and observe a quantum quenching behavior, as well as a Schottky-Ohmic transition, for subnanometre gaps, which enable surface mapping based on this new contrast mechanism. This quantum regime of plasmonic gap-mode enhancement with a few nanometre thick MoS2 junction may be used for designing new quantum optoelectronic devices and sensors with a wide range of applications.

Molybdenum disulfide (MoS 2 ) is a layered 2D TMD material with a graphene-like hexagonal arrangement of Mo and S atoms covalently bonded into single layer S-Mo-S units (Fig. 1b) which are stacked and held together by van der Waals (vdW) interactions 1,2 . The unique mechanical, optical and electronic properties of the monolayer (ML) and few-layer (FL) MoS 2 are attractive for photovoltaic, optoelectronic and sensing applications [3][4][5][6][7][8] . The device performance strongly depends on the quality of materials and contact interfaces which varies on the nanoscale. Therefore, to properly understand and control these materials and devices, it is necessary to study their properties with nanometre spatial resolution. While atomic force microscopy (AFM) 9,10 and scanning tunneling microscopy (STM) [11][12][13] provide rich information about mechanical and electronic properties of TMDs, optical spectroscopic techniques such as photoluminescence (PL) 5,6,14,15 and Raman scattering [16][17][18][19][20][21][22][23] provide important complementary optical information about structure and dynamics. Previous optical studies of MoS 2 grown by chemical vapor deposition (CVD) revealed interesting relaxation properties of edge states and grain boundaries using near-field scanning optical microscopy with > 60 nm resolution 24 . Their PL signals showed ~300 nm wide edge regions and more than 80 nm wide disordered grain boundaries. These results were contrary to the expected ~20 nm atomically-thin termination edge states and were attributed to disorder. Further investigation of these effects requires increasing the spatial resolution and can be performed using other optical techniques such as Raman spectroscopy.
Tip-enhanced Raman scattering (TERS) is a vibrational spectroscopic technique with nanoscale spatial resolution enabled by the local field enhancement of the incident laser field at the nanosize apex of a plasmonic tip [25][26][27][28][29][30] . A major challenge of TERS is to overcome the background signal from the diffraction-limited laser focus. It has been overcome in several cases by placing the sample between the plasmonic substrate and the tip in the so-called "gap-mode" configuration [31][32][33] . Near-field enhancement and the corresponding TERS signals are classically expected to increase with the decrease of the gap between the tip and the sample 25,[34][35][36] , similar to the case Scientific RepoRts | 6:25788 | DOI: 10.1038/srep25788 optical properties. Moreover, since the quantum quenching behavior depends on the material probed, it provides enhanced contrast for surface and edge sensing and mapping.

Results
Tip-enhanced Raman scattering (TERS) of FL-MoS 2 . The schematic of the experimental setup is shown in Fig. 1a. We used a gold coated tip with ~20 nm apex radius to enhance Raman signals from exfoliated FL-MoS 2 flakes deposited on the atomically-flat gold substrate (Fig. 1c). We performed resonant TERS measurements by exciting FL-MoS 2 into the A-exciton band using a 660 nm p-polarized laser (for details see Supplementary Fig. 1). Figure 1d shows the measured optical signals from the location marked with a white dot in Fig. 1c as a function of the tip-sample distance in the units of the sample z-axis displacement (see Fig. 2 for conversion from the sample z-axis displacement to the tip-sample distance). We varied the tip-sample distance from a few nanometres down to a few Angstroms to achieve the maximum signal enhancement. The TERS measurement location marked by the white dot in Fig. 1c corresponds to the MoS 2 thickness of four layers as determined by atomic force microscopy (AFM). At ~4 nm z-axis displacement, the signal intensity suddenly increases leading to the so-called "snap to contact" (see below) 44 . At that moment, the actual distance between the tip and the sample is ~3 nm. The thickness of the four-layer MoS 2 is ~2.7 nm. Therefore, the distance between the tip and the gold substrate is ~5.7 nm, which gives rise to the plasmonic gap mode which is crucial for signal enhancement due to formation of the electric field hot spots in the tip-substrate gap [31][32][33] . No tip enhancement was observed in similar experiments using the gold tip from FL-MoS 2 deposited on a glass substrate. Figure 1e shows the spectra before (tip-sample distance ~5.8 nm, red) and after (tip-sample distance ~0.33 nm, green) the contact between the tip and the FL-MoS 2 . The observed transitions are assigned to the two first-order Raman-active vibrational modes at the Γ point of the Brillouin zone (BZ): in-plane E g 2 1 and out-of-plane A g 1 at 382 cm −1 and 408 cm −1 , respectively 58 . The mode at 177 cm −1 is the difference combination mode of the out-of-plane and longitudinal acoustic phonon at the M point: 22,58 . The spectra in the range between 450 cm −1 and 490 cm −1 show a double mode feature. The most pronounced mode at 464 cm −1 is the A u 2 mode, while the mode on its shoulder is associated with the LA M ( ) phonon 58 . In the spectral range higher than 490 cm −1 , there are four second-order modes at 526 cm −1 ( ( 58 . These different modes were enhanced by different factors due to their different polarization selection rules. When the tip approaches the sample it causes depolarization of the incident p-polarized laser field which leads to the enhancement of, for example, s-polarized in-plane modes. The estimated enhancement factors (EFs) of the strongest modes are given in Supplementary Fig. 7 and Supplementary Table 1. The in-plane E g 2 1 mode shows the largest enhancement due to the depolarization of the incident laser field by the tip. The dashed lines in Fig. 1e show the fittings of the photoluminescence (PL) background signals.

Subnanometre-gap dependence with sub-Angstrom control. Resonant excitation of surface plas-
mons by a metallic tip near the metallic surface gives rise to a large electric field enhancement described by the image charge model 59 . We investigate the dependence of the signal enhancement on the tip-sample distance by approaching the gold tip to gold, FL-MoS 2 , and carbon nanotube (CNT) samples with sub-Angstrom precision. This is achieved by decreasing the tip-sample distance using contact-mode AFM force-distance measurements (Fig. 2). Figure 2a shows the applied cantilever force as a function of the sample z axis (piezo) displacement during the tip-sample approach. At ~4 nm displacement, the gradient of the tip-sample force exceeds the elastic constant of the cantilever and the tip jumps onto the sample surface in the so-called "snap to contact" 60 . Afterwards, the movements of the tip and the sample are linearly coupled which is reflected by the straight "contact line. " We denote the starting point of the contact line as "vdW contact" as the onset of the localized repulsive force which manifests that the tip-sample distance reached the vdW diameter (~0.3 nm). After the vdW contact, the total force on the sample remains attractive for a while as adsorbed molecules, such as water vapor under ambient conditions, contribute to the adhesive force. Figure 2b shows the displacement-repulsive force curve after the vdW contact resulting from the subtraction of the adhesive force from the total applied force. The spike at ~10.7 nm displacement on the curve with ~30 nN repulsive force indicates that the tip penetrated the MoS 2 flake 61 . Therefore, for the tip-sample distance dependence analysis below we only consider the data before this breaking point. We obtain the tip-sample distance control before the vdW contact from the linear relation between the applied force and the cantilever deflection with the accuracy of ~0.16 nm (see Supplementary Fig. 3). However, after the vdW contact, we use the repulsive force from the Lennard-Jones model ( ) to convert the repulsive force into the tip-sample distance with sub-Angstrom accuracy of ~0.0014 nm (see Supplementary Fig. 4). We determine the value of A = 2.2 × 10 −7 nN nm 13 at the breaking point when the distance between Au and S atoms is close to the sum of their radii ~2.42 Å (Ref. 62). Figure 2c shows the corresponding conversion of the repulsive force into distance. More details are given in Supplementary Fig. 2 and Supplementary Note 1. Figure 3a shows the measured PL intensity of the gold tip in the vicinity of the atomically-flat gold substrate at 1.82 eV (~510 cm −1 ) increasing with the decrease of the tip-sample distance before the vdW contact as predicted by the classical model. At ~2 nm separation, the PL intensity steeply increases, and reaches the maximum when the tip contacts the sample at ~0.33 nm corresponding to the typical Au vdW diameter. Afterwards, the cantilever deflection increases linearly with the decrease of the tip-sample distance, due to the increase of the repulsive force between the tip and the sample (see Fig. 2 and Supplementary Fig. 2), accompanied by the rapid decrease of the PL as predicted by the quantum model. Similar PL quenching of the gold tip near a gold substrate was previously observed using a combination of AFM and scanning tunneling microscopy (STM) and was attributed to be due to quantum tunneling and nonlocal effects 48 . However, our experiments are performed using only AFM without bias which could explain the differences in the onset of the PL quenching and in the distance dependence of the Raman signals. We used the same tip to repeat the distance-dependence measurements several times to confirm reproducibility. The reproducible results shown in Supplementary Fig. 5 prove that the tip was not broken during the measurements. As the tip-sample distance decreases to the vdW diameter, an effective electron wave function overlap between the tip and the substrate is established, forming a conductive tunneling junction. The capacitive coupling before the contact is reduced by the conduction current between the tip and the substrate leading to charge transfer plasmons 37,63,64 . The classical coupling of the tip and substrate via image charges results in the large near field enhancement in few nanometre gaps 31 . The conduction current in the gap suppresses the charge accumulation on the surfaces, decreasing the near fields and quenching the PL signals at subnanometre gaps in the quantum coupling regime. These classical and quantum coupling schemes are shown for the gold tip coupled to the gold substrate in Fig. 3d.
Quantum plasmonic regime of the near field and optical signal enhancement in coupled metallic nanostructures has been well explored 47,49 . Here we investigate the corresponding quantum limit in the hybrid system consisting of the FL-MoS 2 between two gold surfaces. Figure 3b shows the tip-sample distance-dependence of the FL-MoS 2 sample PL at 1.82 eV and Raman signal at 177 cm −1 . Both signals increase with the decrease of the tip-sample distance before the vdW contact, as in the case of the gold substrate PL. However, after the vdW contact the distance-dependences for the FL-MoS 2 and gold substrates are different. There is a sharp turnover point for the PL from gold at the moment of vdW contact, whereas the FL-MoS 2 signals stay nearly constant and start decreasing for the tip-sample distances smaller than the vdW diameter. The quench and vdW contact occur at the gap sizes of ~0.27 and 0.32 nm, respectively, for FL-MoS 2 , while they both occur at the same gap size of ~0.33 nm for gold. Figure 3c shows a control measurement of the distance-dependent PL and Raman signals for the G band of the carbon nanotube (CNT) on the gold substrate. There is no significant quenching after the vdW contact. Figure 3f indicates that the ~1.2 nm CNT diameter is smaller than the tip apex curvature. Therefore, the bonding charges are transferred only partially, which corresponds to the screened plasmon modes and a small decrease of the field enhancement. However, the CNT-gold junction forms a Schottky contact with ~0.3 eV Schottky barrier height (SBH) and suppressed electron injection 65  Subnanometre-gap nanoimaging. Figure 4 shows subnanometre-gap tip-enhanced nanoimaging of another FL-MoS 2 flake. A region highlighted by the black rectangle in the AFM image in Fig. 4a was chosen for spatial mapping of the tip-induced optical signals in Fig. 4b,c. The force applied by the tip on the sample was  Fig. 4b shows a high contrast with the enhanced PL signal at the edge of the FL-MoS 2 flake and quenching on the gold substrate and on the inner area of the flake. These effects are attributed to the subnanometre-gap quantum regime. Quenching of the PL emission of the gold tip on the gold substrate is stronger than on the FL-MoS 2 , resulting in a high imaging contrast. Figure 4d shows the AFM (solid line), PL (open circles) and Raman (red filled circles) profiles across the edge of the MoS 2 flake which correspond to the yellow dashed line in Fig. 4a. The maxima of the PL and Raman profiles occur at the edge of the flake, where only a part of the tip is in contact. Figure 4e shows the corresponding model of the partially screened subnanometre gap plasmon imaging. Only the charges in the vicinity of the gap flow through the junction reducing the quenching effect. Therefore, the tip-induced signals are quenched both on the gold substrate and on the inner part of the flake but the quenching is suppressed at the edge. The thickness of the FL-MoS 2 in the highlighted black rectangle is ~2.8 nm which corresponds to four layers. The size of the observed FL-MoS 2 optical edge profile is ~20 nm which corresponds to the size of the tip but is significantly smaller than the size of the excitation laser spot (~1 μ m). This edge profile was used to estimate the TERS spatial resolution of ~20 nm (see Supplementary Fig. 6).

Discussion
Several mechanisms can explain the decrease of the tip-enhanced optical signals at subnanometre gaps. Classical resonance energy transfer and quantum tunneling (QT) effects quench PL at large and small gaps, respectively 48 . However, both mechanisms have no direct influence on the Raman scattering process due to its nearly instantaneous relaxation. Most commonly, the quench of the Raman signals is due to the decrease of the electric fields in the gap which strongly relies on the capacitive coupling between the tip and the substrate. Quantum tunneling between the gold tip and the FL-MoS 2 can reduce the charge accumulation on the surface of the tip and decrease the corresponding electric fields 68 . Figures 3d-f show the coupling schemes in the three investigated sample configurations. The FL-MoS 2 -gold system is described as a metallic sphere-plane configuration with the FL-MoS 2 conductive junction, whose conductivity impacts the optical response of the system 69 . For high conductivity and large aspect ratio, charge transfer plasmons can be generated. For partial coverage of the junction, the charge transfer takes place in the vicinity of the junction, giving rise to screened plasmons with partial charges at both metallic surfaces 69 . This requires an abundant number of carriers on both sides of the junction, which may be increased due to photo-excitation. Previous work showed that MoS 2 photocurrent can be enhanced by surface plasmons of gold nanoparticles 70 . However, for metal-semiconductor junctions, the SBH also significantly impacts the conductive electron injection. The SBH of the FL-MoS 2 -gold junction is low and favorable for the electron injection (~50 meV) 10,71 . However, formation of the Ohmic contact is sensitive to the distance between the metal and MoS 2 . The hybridization and overlap of the electron wave functions between the Au and Mo atoms play a dominant role in the electron injection from the gold tip to MoS 2 62 . The distance between the Mo and S atomic layers in the monolayer MoS 2 is ~0.24 nm. When the gold tip contacts the S atomic layer, the distance between the Au atoms at the tip apex and the Mo atoms beneath the first S atomic layer is larger than the vdW diameter. The corresponding SBH is larger than 50 meV preventing the formation of the Ohmic contact. However, even though the tip gets closer to the MoS 2 surface by only 0.06 nm which still cannot make a good contact between the Au and Mo atoms, an effective electrical contact can be formed between the gold tip and the MoS 2 sample due to the formation of the gap state, as S atoms mediate the hybridization between the Au and Mo atoms 72 . This mechanism can explain why the quench of the FL-MoS 2 tip-enhanced signals and the vdW contact do not take place simultaneously. In contrast, when the gold tip gets in contact with the gold surface at the vdW diameter separation, the effective overlap of the electron wave functions between the tip and the substrate gives rise to the effective electron injection. For the FL-MoS 2 junction, the formation of the gap state requires a shorter distance than the vdW diameter 72 . Figure 3b provides evidence for the formation of an Ohmic contact in the FL-MoS 2 -gold junction when a stronger force is applied at subnanometre gaps. This makes MoS 2 an attractive material for conductive junctions.
In summary, we demonstrated the first tip-enhanced Raman scattering signals of FL-MoS 2 on a gold substrate, which revealed the quantum coupling regime. We showed a new approach for studying the nanooptical properties of gold-MoS 2 junctions via tip-sample distance dependence of subnanometre-gap Raman and PL signals. This allowed for distinguishing ~20 nm edge states and nanoscale inhomogeneous structural features in FL-MoS 2 . The observed quantum quenching behavior depends on the material probed and provides enhanced contrast for surface sensing and mapping. This quantum imaging contrast can be used for future studies of grain boundaries and defects in 2D materials. Quantum coupling can also be used to enhance the sensitivity of single molecule imaging when the substrate is non-metallic. Subnanometre-gap Ohmic contacts and quantum plasmonic effects may be used to improve the performance of MoS 2 -based devices such as Schottky diodes and phototransistors. Other techniques can be used to further enhance the near fields and Raman signals based on coherence 73 and gain 74 . Quantum plasmonic nanoimaging may be combined with high-resolution TEM 75,76 to provide complementary information about the atomic structural defects and their optical properties. Our work opens new possibilities to explore quantum effects in plasmonic chemical sensors and photo-devices based on 2D materials.

Methods
Materials and sample preparation. Tips were gold coated (AIST NT) with ~20 nm apex radius. FL-MoS 2 flakes were prepared using mechanical exfoliation from molybdenite (SPI), and were deposited on the atomically-flat Au/SiO 2 substrate (Platipus). Single-wall carbon nanotubes (~70% metallic) on atomically-flat gold substrate were provided by AIST-NT.
Tip-enhanced Raman scattering (TERS). All atomic force microscopy (AFM) and TERS measurements were performed using a combined scanning probe microscopy (SPM) system (OmegaScope-R, AIST-NT) and a Raman microscope (LabRAM HR4000, Horiba). Tapping-mode AFM was used for measuring sample topography. Contact-mode AFM was used for TERS distance-dependence and imaging measurements. A cw diode laser (659.38 nm, 1.88 eV) was focused onto the gold tip apex with an objective lens (NA = 0.9) in the side illumination, polarized along the tip axis. The signal was collected in the backscattering configuration with a long-pass 661.56 nm edge filter, and was detected with a grating spectrometer coupled to a CCD camera. Reproducibility of TERS measurements was checked on several samples (see Supplementary Fig. 5)