Splitting of monolayer out-of-plane $A_1^{\prime }$ Raman mode in few-layer ${\mathrm{WS}}_2$

We present Raman measurements of mono- and few-layer ${\mathrm{WS}}_2$. We study the monolayer $A_1^{\prime }$ mode around $420{\mathrm{cm}}^{-1}$ and its evolution with the number of layers. We show that with increasing layer number there are an increasing number of possible vibrational patterns for the out-of-plane Raman mode: in $N$-layer ${\mathrm{WS}}_2$ there are $N$ $\mathrm{\Gamma }$-point phonons evolving from the $A_1^{\prime }$ monolayer mode. For an excitation energy close to resonance with the $A$ excitonic transition energy, we were able to observe all of these $N$ components, irrespective of their Raman activity. Density functional theory calculations support the experimental findings and make it possible to attribute the modes to their respective symmetries. The findings described here are of general importance for all other phonon modes in ${\mathrm{WS}}_2$ and other layered transition-metal dichalcogenide systems in the few-layer regime.

Figure 1

(a) Optical micrograph of a ${\mathrm{WS}}_2$ flake with selected regions inspected by AFM [shown in (b) and (c)]. (b) and (c) AFM images of the selected regions with indication of layer numbers and lines showing where AFM height profiles were taken from. (d) AFM height profiles going from the substrate onto the flakes for different positions on the flake. Step heights in units of the observed interplanar spacing of $\sim 0.7$ nm are indicated.

Figure 2

(a) Raman spectra of FL ${\mathrm{WS}}_2$ from one (1L) to five (5L) layers and the bulk material (NL). Excitation wavelength is 457 nm. Spectra are normalized to the intensity of the $A$ mode at $420{\mathrm{cm}}^{-1}$. (b) Evolution of the frequency of the main $E$ and $A$ modes with the number of layers. The dashed line marks the increasing frequency difference between the modes with the number of layers. (c) Strong photoluminescence is observed for monolayer ${\mathrm{WS}}_2$ at the direct excitonic transition energy around 625 nm. The inset shows a magnified image of the same spectrum in the region of the main 1L-${\mathrm{WS}}_2$ Raman peaks.

Figure 3

Experimental resonance Raman spectra (excitation wavelength 633 nm) of the $A$-mode region in FL-${\mathrm{WS}}_2$ from the bilayer (2L) to five layers (5L) and the bulk (NL). The monolayer spectrum (1L) is only shown with an excitation wavelength of 457 nm, as the Raman features are dominated by strong photoluminescence at 633-nm excitation spectrum (not shown). For FL-${\mathrm{WS}}_2$, spectra of the same region taken with the 457-nm excitation wavelength are overlaid and depicted with dashed lines. Spectra are normalized to the main Raman peak and are offset for clarity.

Figure 4

Experimental resonance Raman spectra of FL-${\mathrm{WS}}_2$. The Lorentzian fit curves are shown as well as the symmetry attributed to the individual modes. In general, there are $N$ components for an $N$-layer spectrum. (a) For an even number of layers, Raman-active $A_{1g}$ modes alternate with infrared-active $A_{2u}$ modes. (b) For an odd number of layers, Raman-active $A_1^{\prime }$ modes alternate with infrared $A_2^{\prime \prime }$ modes. For both even and odd $N$, the Raman-active modes are more intense than the rather weak infrared-active modes.

Figure 5

Schematic drawing for all possible vibrational modes in the out-of-plane mode region of FL-${\mathrm{WS}}_2$ (Raman and infrared) for one (1L) to five (5L) layers together with the symmetry assignments taken from our DFT calculations. The displacement patterns are ordered with increasing frequency from left to right. Taking into account the full set of possible vibrational patterns helps us to study the splitting of vibrational modes with increasing layer number and to attribute the modes to the features seen in the Raman spectra.

Figure 6

(a) Raman frequencies of the $A$-type modes in FL-${\mathrm{WS}}_2$. Red circles mark the Raman-active modes; blue squares denote the infrared-active modes also seen in the Raman spectra. Dashed lines are used to guide the eye. Starting from one layer, the splitting of the modes for FL-${\mathrm{WS}}_2$ produces a fanlike shape of the possible vibrational frequencies. (b) Theoretical calculations with DFT reproduce the observed trends. Raman-active modes are denoted with open red circles; infrared-active modes are marked with open blue squares.