Comprehensive optical characterization of atomically thin ${\mathrm{NbSe}}_2$

Transition-metal dichalcogenides (TMDCs) have offered experimental access to quantum confinement in one dimension. In recent years, metallic TMDCs like ${\mathrm{NbSe}}_2$ have taken center stage with many of them exhibiting interesting temperature-dependent properties such as charge density waves and superconductivity. In this paper, we perform a comprehensive optical analysis of ${\mathrm{NbSe}}_2$ by utilizing Raman spectroscopy, differential reflectance contrast, and spectroscopic ellipsometry. These analyses, when coupled with Kramers-Kronig analysis, allow us to extract the dielectric functions of bulk and atomically thin ${\mathrm{NbSe}}_2$ and relate them to the resonant behavior of the Raman spectra.

Figure 1

(a) An illustration of the crystal structure of monolayer 2H-${\mathrm{NbSe}}_2$, along with (b) an optical image of an example flake mechanically exfoliated onto Si/${\mathrm{SiO}}_2$. The area containing the monolayer (1L) flake is enclosed by a dashed green line. (c) Raman results for 1L, 2L, 3L, and bulk ${\mathrm{NbSe}}_2$ for an excitation wavelength of 514 nm. The dashed dark cyan and orange lines are meant to guide the eye to the bulk ${\mathrm{A}}_{1\mathrm{g}}$ and ${\mathrm{E}}_{2\mathrm{g}}$ modes, respectively. (d) The positions of the ${\mathrm{A}}_{1\mathrm{g}}$ and ${\mathrm{E}}_{2\mathrm{g}}$ modes are plotted as a function of layer number (left vertical axis) with dark cyan and orange points, respectively. The separation of the two modes (labeled on the right vertical axis) is shown with a set of crosses. The insets are visualizations of the mode vibrations.

Figure 2

(a) Raman spectra are acquired for several wavelengths for 1L, 2L, 3L, and bulk ${\mathrm{NbSe}}_2$. The gray, blue, and orange bands highlight regions where the soft mode, ${\mathrm{A}}_{1\mathrm{g}}$, and ${\mathrm{E}}_{2\mathrm{g}}$ modes are observed, respectively. For the case of bulk, the soft mode and the ${\mathrm{E}}_{2\mathrm{g}}$ mode are amplified by a factor of 4 for clarity in the 633-nm spectrum. (b) The resonance Raman data are summarized by their peak positions in the top panel, with the blue and orange bands still indicating the ${\mathrm{A}}_{1\mathrm{g}}$ and ${\mathrm{E}}_{2\mathrm{g}}$ modes, respectively. The bottom panel shows the relative intensities of ${\mathrm{E}}_{2\mathrm{g}}$ and ${\mathrm{A}}_{1\mathrm{g}}$, with the inset showing the relative intensity of ${\mathrm{A}}_{1\mathrm{g}}$ with respect to the silicon peak as measured through the oxide layer.

Figure 3

(a) The Raman spectra of bulk ${\mathrm{NbSe}}_2$ acquired at 4 K for four different wavelengths. In this figure, all dashed dark cyan and orange lines indicate the ${\mathrm{A}}_{1\mathrm{g}}$ and ${\mathrm{E}}_{2\mathrm{g}}$ modes, respectively. (b) Raman spectra as a function of temperature for 514-nm excitation. (c) Raman peak positions, FWHMs, and normalized intensities plotted for two wavelengths (indicated by different symbols) as a function of temperature. (d) Resistance of a bulk ${\mathrm{NbSe}}_2$ device plotted as a function of temperature, with different color curves representing different magnetic field values.

Figure 4

(a) The DRC spectra for bulk and thin ${\mathrm{NbSe}}_2$ are shown. These spectra are converted into absorption to obtain an initial guess for ${\varepsilon }_2$. (b) In the case of bulk ${\mathrm{NbSe}}_2$, its DRC spectrum is converted and undergoes KKA, with the resulting ${\varepsilon }_{\mathrm{bulk}}\left(E\right)$ shown in the top and middle panels as their real (blue) and imaginary (green) components, respectively. This result is compared with the direct measurement of ${\varepsilon }_{\mathrm{bulk}}\left(E\right)$ by SE, the real and imaginary components of which are also in the top (orange curve) and middle (purple curve) panels, respectively. The bottom panel shows the original bulk DRC spectrum (light blue), as well as two generated DRC curves. The pink and yellow curves are obtained when regenerating a DRC spectrum with the KKA-extracted and SE-extracted dielectric functions, respectively. (c) The KKA-extracted dielectric functions are shown for bulk, 3L, 2L, and 1L ${\mathrm{NbSe}}_2$. The real and imaginary components are represented by orange (left vertical axis) and purple (right vertical axis) curves, respectively.