Exciton Mapping at Subwavelength Scales in Two-Dimensional Materials

Spatially resolved electron-energy-loss spectroscopy (EELS) is performed at diffuse interfaces between ${\mathrm{MoS}}_2$ and ${\mathrm{MoSe}}_2$ single layers. With a monochromated electron source (20 meV) we successfully probe excitons near the interface by obtaining the low loss spectra at the nanometer scale. The exciton maps clearly show variations even with a 10 nm separation between measurements; consequently, the optical band gap can be measured with nanometer-scale resolution, which is 50 times smaller than the wavelength of the emitted photons. By performing core-loss EELS at the same regions, we observe that variations in the excitonic signature follow the chemical composition. The exciton peaks are observed to be broader at interfaces and heterogeneous regions, possibly due to interface roughness and alloying effects. Moreover, we do not observe shifts of the exciton peak across the interface, possibly because the interface width is not much larger than the exciton Bohr radius.

Figure 1

EELS experiments have been performed in scanning transmission mode where a narrow electron beam (yellow cone, width $R\sim 1\mathrm{nm}$) is used to probe excitons across a diffuse interface. For the pure regions, the area probed will be limited by the size of the exciton wave function (represented by ellipses), as it is larger than $R$, and delocalization effects. Interestingly, using a narrow electron probe allows access to the energy-loss spectrum of materials at scales far below the wavelength of the emitted light (arrows in the drawing).

Figure 2

(a) HAADF images of a ${\mathrm{MoS}}_{2(1-x)}{\mathrm{Se}}_{2x}$ layer. (b) Example of a region with a sharper interface, which can be found locally. (c)–(f) Chemical mapping of a nanometrically mixed region of ${\mathrm{MoS}}_2$ and ${\mathrm{MoSe}}_2$. (c)–(f) shows the HAADF, the S $L$ map, the Se $M$ map, and the S $L$ and Se $M$ edges respectively. (g) Low loss EELS spectra of ${\mathrm{MoS}}_2$ (purple) and ${\mathrm{MoSe}}_2$ (orange). Two main features are seen. The first one, marked $A$, is associated with excitons. It is split in two energy-loss peaks due to spin-orbit coupling [5]. The second feature, marked $B$, is also associated with an exciton. The red curve is a photoluminescence spectrum taken from the heterogeneous sample shown in (a).

Figure 3

(a) Typical HAADF image of ${\mathrm{MoS}}_2\text{−}{\mathrm{MoSe}}_2$ interfaces, showing a diffuse chemical profile. (b) Maps of the fitting coefficients for ${\mathrm{MoS}}_2$ (above) and ${\mathrm{MoSe}}_2$ (below). (c) Comparison of the fitting coefficient profiles from with the chemical profiles measured from core-loss EELS of the S $L$ and Se $M$ edges. (d) Five spectra integrated at different positions across the interface, with positions marked by colored squares and numbers in (b). (e) Projection of the EELS map in the spatial direction perpendicular to the interface. The change from ${\mathrm{MoS}}_2$ to ${\mathrm{MoSe}}_2$ is followed by peak broadening but no apparent spectral shift.

Figure 4

(a) Maps of the fitting coefficients for ${\mathrm{MoS}}_2$ (above) and ${\mathrm{MoSe}}_2$ (below) extracted using a multiple linear fit algorithm. (b) HAADF profile associated with the maps in (a) [the scales in (a) and (b) are identical]. The HAADF profile, proportional to a power of the local composition, changes in a distance shorter than 5 nm along the interface. (c) Three spectra integrated in regions across the interface. The distance between them is about 10 nm. Changes of the exciton energy-loss spectra can be observed even in this deep subwavelength regime.