Probing nanoscale variations in strain and band structure of $\mathrm{Mo}{\mathrm{S}}_2$ on Au nanopyramids using tip-enhanced Raman spectroscopy

We report tip-enhanced Raman spectroscopy and tip-enhanced photoluminescence studies of monolayer and bilayer $\mathrm{Mo}{\mathrm{S}}_2$ in which we characterize photoluminescence and first- and second-order Raman spectra in monolayer, bilayer, and inhomogeneously strained $\mathrm{Mo}{\mathrm{S}}_2$. From the transition of unstrained $\mathrm{Mo}{\mathrm{S}}_2$ from monolayer to bilayer, we determine a spatial resolution of approximately 100 nm through the peak positions of the first-order Raman modes. The strain dependence of the second-order Raman modes reveals changes in the electronic band structure in strained $\mathrm{Mo}{\mathrm{S}}_2$ that are directly observed through changes in the Raman peak positions and peak area ratios, which are corroborated through density functional theory calculations.

Figure 1

(a) Schematic diagram of the experimental geometry for TERS measurements of $\mathrm{Mo}{\mathrm{S}}_2$ draped over Au nanopyramid structures. (b) SEM image of a representative Au tip used for TERS and TEPL measurements. Raman spectra obtained with the Au AFM probe in tapping mode (red curve) and in soft contact with the sample surface (black curve) with a 300 grooves/mm grating from (c) monolayer $\mathrm{Mo}{\mathrm{S}}_2$ and (d) bilayer $\mathrm{Mo}{\mathrm{S}}_2$.

Figure 2

(a) TERS spectrum from bilayer $\mathrm{Mo}{\mathrm{S}}_2$ taken with an 1800 grooves/mm grating. The TERS spectrum has been fit to seven Lorentzian peaks with the numerical labels corresponding to vibrational modes listed in Table 1. The sum of the fitted peaks is shown in gray and shows excellent agreement with the measured spectrum. (b) Schematic drawing of an example DRR process in which an incident photon of energy $E_L$ first excites an electron-hole pair in the $K$ valley; then the excited electron is scattered to the $K$′ valley through the emission of the phonon, as shown with the green arrow. The excited electron is then scattered back to the $K$ valley through the emission of a second phonon, as shown with the blue arrow. Finally, the electron-hole pair recombines and emits a photon.

Figure 3

Contour maps of the conduction band edge energy minimum calculated from density functional theory band structure simulations for (a) monolayer ($a=3.2139\AA$) and (b) bilayer ($a=3.2201\AA$) $\mathrm{Mo}{\mathrm{S}}_2$. We take $E=0$ to be at the corresponding top of the valence band in monolayer and bilayer $\mathrm{Mo}{\mathrm{S}}_2$. (c) Cut of the band structure along the high-symmetry directions in k for unstrained (black curve), −0.5% applied hydrostatic strain (red curve), and +0.5% applied hydrostatic strain bilayer (blue curve) $\mathrm{Mo}{\mathrm{S}}_2$. The high-symmetry points (Γ, $Q, K, M$) are indicated by the green dashed lines.

Figure 4

(a) AFM image of $\mathrm{Mo}{\mathrm{S}}_2$ transferred onto a flat Au substrate. The solid white line cut traverses a transition from a bilayer to a monolayer region, delineated by the white dashed line. (b) AFM topography for the white line cut shown in (a). The blue and red lines highlight the bilayer and monolayer regions, respectively, with a step height between the regions of ∼0.6 nm. TEPL and TERS measurements taken along the line cut in (a) across the monolayer to bilayer transition region. The blue and red lines highlight the average constant values in the bilayer and monolayer regions. (c) Top panel: Position of the PL peak associated with the $A$ exciton and trion (black points) and peak PL intensity (blue points) along the line cut. Bottom panel: Raman peak positions for the second-order Raman modes associated with the Van Hove singularity in the phonon DOS and scattering of electrons by longitudinal acoustic phonons near the $K$ and $M$ points in the BZ. (d) Raman peak positions for (top panel) first-order out-of-plane $A_{1g}$ mode and (bottom panel) second-order in-plane $E_{2g}^1$ mode. The insets for the top and bottom panels show schematic drawings for the movement of the atoms in the corresponding vibrational modes.

Figure 5

(a) SEM image of successfully transferred $\mathrm{Mo}{\mathrm{S}}_2$ on a patterned Au nanopyramid array. Areas covered by $\mathrm{Mo}{\mathrm{S}}_2$ appear darker in the image. (b) An AFM image and line cut of bilayer $\mathrm{Mo}{\mathrm{S}}_2$ draped over a Au nanopyramid. (c) AFM topography along the blue line cut in (b). Arrows indicate spatial position where TERS and TEPL measurements were taken. (d–f) TEPL spectra taken at points corresponding to the labeled arrows in (c). The black baseline PL spectrum is taken at the point indicated by the circled arrow.

Figure 6

(a) Top panel: AFM topography of the line cut shown previously in Fig. 5. Raman peak positions of the first-order (second panel) $E_{2g}^1$ and (bottom panel) $A_{1g}$ vibrational modes along the nanopyramid line cut. The insets show schematic drawings of the movement of the atoms for the corresponding vibrational modes. (b) Raman peak positions (with error bars) of the second-order modes along the line cut (AFM topography shown in the top panel) related to (second panel) longitudinal and transverse acoustic phonon scattering of electrons near the $K$ point in the BZ and (third panel) only longitudinal acoustic phonon scattering of electrons near the $K$ point. Bottom panel: Raman peak areas (with error bars) of the second-order mode associated with LA phonon scattering of excited electrons near the $K$ point in the BZ (black squares) and the second-order mode associated with LA phonon scattering of excited electrons near the $M$ point in the BZ (red circles). (c) Phonon dispersion for the acoustic phonon modes calculated using DFT simulations for unstrained (blue curve), +0.5% applied hydrostatic strain (red curve), and +1.0% applied hydrostatic strain (orange curve) bilayer $\mathrm{Mo}{\mathrm{S}}_2$. The phonon modes represent the out-of-plane (ZA), in-plane transverse (TA), and in-plane longitudinal (LA) acoustic vibrational modes. The high-symmetry points (Γ, $Q, K, M$) are indicated by the green dashed lines.