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Visualization of Band Shifting and Interlayer Coupling in WxMo1-xS2 Alloys using Near-Field Broadband Absorption Microscopy

Beyond-diffraction-limit optical absorption spectroscopy provides profound information on the graded band structures of composition-spread and stacked two-dimensional materials, in which direct/indirect bandgap, interlayer coupling, sliding, and possible defects significantly modify their optoelectronic functionalities such as photoluminescence efficiency. We here visualize the spatially-varying band structure of monolayer and bilayer transition metal dichalcogenide alloys for the first time by using near-field broadband absorption microscopy. The near-field-spectral and -spatial diagrams manifest the excitonic band shift that results from the interplay of composition spreading and interlayer coupling. These results enable us to identify the top layer of the bilayer alloy as pure WS2. We also use the aberration-free near-field transmittance images to demarcate the exact boundaries of alloyed and pure transition metal dichalcogenides. This technology can offer new insights on various layered structures in the era of stacking science in quest of novel quantum optoelectronic devices.

illumination in far-field confocal microscopy [33] is a major hurdle to achieve high lateral absorption resolution, especially when multilayered or stacked areas of the sample are a few m in size.
To overcome the above aberration problem in absorption mapping [34], the aperture-type scanning near-field optical microscopy (a-SNOM) provides an aberration-free, sub-diffraction-limit light spot. The a-SNOM has so far been used to optically visualize point defects, grain boundaries, and lateral heterostructures of TMDs through near-field PL mapping [35][36][37][38]. We here show that near-field absorption spectroscopy, equipped with sub-diffraction-limit spatial resolution, can provide fully-spectroscopic excitonic information, which has never been realized for TMDs up to now.
In this study, we use near-field broadband absorption microscopy to visualize the spatially-varying band shifting and interlayer coupling of monolayer TMD alloy, WxMo1-xS2.
The spatial distribution of its excitonic bands is reconstructed from the mapping of near-field transmittance (NF-tr). The energy-location diagrams, which reflect the electronic structure of TMD alloy, reveal the energy shifting of A, B, and C excitons along a lateral spatial profile. In the case of bilayer WxMo1-xS2 alloy, the energy-location diagrams confirm that the top layer is pure WS2, and the excitonic band shifting is induced by the interlayer coupling. In addition, we show that NF-tr images at different photon energies can demarcate pure TMD from alloyed with clear-cut boundaries. These results demonstrate that, to investigate the stacking and interlayer coupling of 2D materials, near-field absorption microscopy provides a powerful tool to produce aberration-free and nanoscale-resolution imaging of the band structure over a wide range of energy, even in the presence of highly lateral inhomogeneity. 6

Results and Discussion
We show in Figs. 1a and 1a' the optical pathways of far-field transmittance (FF-tr) and near-field transmittance (NF-tr) measurements. For FF-tr, the top objective lens focuses the white light source, while the bottom objective lens collects the transmitted light. However, the chromatic aberration prevents the lens from focusing the broadband light into the same spot; so, a clear contrast can only be achieved within a narrow wavelength range. In the case of NF-tr, the a-SNOM tip limits the amount and lateral size of light though the aperture hole, as shown in  The WxMo1-xS2 alloy was synthesized by tuning the growth temperature and reactant supplement in one-pot CVD growth [39]. Pure MoS2 is located at the center of the triangular nanosheet, with the fraction of W atoms (denoted as x) gradually increasing from x = 0 at the center to x = 1 at the outer edges. The band shift for WxMo1-xS2 can be deduced from a simple type-II band alignment between pure MoS2 and pure WS2, with gradient band transition in 7 between [40]. The bandgap varies as a function of the compositional fraction, x, exhibiting a location-dependent spectral shift. Continuous PL peak shifting with compositional fraction has been observed by confocal PL spectroscopy of TMD alloys [14,[18][19][20][21][22]32]. The correct interpretation of NF-tr images, however, requires a series of NF-tr spectra.  Fig. 1e'). The A exciton induces a transmittance dip of 3-6%: for pure WS2, the A exciton band is located at 2.03 eV, but it redshifts to 1.90 eV for pure MoS2. As for the B exciton, the absorption dip that it induces is only 2-3%, with its band shifting from 2.40 eV for pure WS2 to 2.12 eV for pure MoS2.  During alloy growth, the x fraction value typically varies along the growth direction (location). Yet, in most circumstances, this value tends to depend linearly on the location. The x value is commonly extracted from the A exciton band-shift in the PL spectra [19][20][21][22][23]. However, the determination of the pure-alloy MoS2 boundary (x = 0) is not easy. As shown in Fig. 2c, the 9 A exciton band-shift would lead us to mark the region of pure MoS2 (x = 0) from location L= 5.5 to 11.5 m. We however note that the x = 0 region provided by the B exciton band-shift is significantly narrower by comparison, with the discernable flat-band region only ranging from L = 7 to 8 m. The main difficulty in precisely tracking the exciton band evolution lies in the fact that the dependence of the composition fraction on location may not be linear. The difference of the flat-band regions obtained from the A and B excitons certainly renders the value of x extracted from the PL spectra questionable. Since this redshift is not linear in the energy-location diagram, a bowing factor, b, is introduced to evaluate the deviation from linearity, namely the curvature [14,21,32,41,42]. The exciton energy curves are fitted to the following quadratic equation where ( ) denotes the exciton energy for a specific x value, To go further, we calibrate the nonlinearity between and location ( ) by introducing a power n according to where 0 stands for the distance between pure WS2 and pure MoS2. The fitted n value is close to 1 (1.02 for the A exciton and 1.00 for the B exciton), hence proving that x is linear with the location, as expected.
Having understood the NF-tr energy-location diagram of Fig. 2c, it now becomes straightforward to interpret the NF-tr images given in Figs. 1b'-1f'. For photon energy h = 2.64 eV (Fig. 1b'), the central MoS2 part exhibits a particularly low transmittance dip due to the C exciton of MoS2. At h = 2.38 eV (Fig. 1c') and 2.03 eV (Fig. 1d'), the NF-tr images highlight the WS2 part at the outer edges due to the B and A excitons of WS2. At h =1.97eV ( Fig. 1e'), only a narrow dark absorption stripe appears at a particular x fraction of WxMo1-xS2.
Finally, at h =1.88eV (Fig. 1f'), pure MoS2 hosts such a low-lying A exciton that corresponds to the dark triangle in the center. All this demonstrates that the NF-tr spectra and images are powerful tools to resolve the spatial variance of the complicated band structure of monolayer TMD alloys.
After considering the monolayer TMD alloy, we now extend the methodology to the more complicated case of bilayer TMD alloy. Here again, NF-tr and near-field photoluminescence (NF-PL) techniques prove valuable in determining the layer number and the interlayer coupling.  Blue and red lines stand for the excitons coming from 1st-L WS2 and 1st-L MoS2, respectively.
Orange lines indicate the shifted bands due to interlayer coupling. Mo-rich alloy regions by near-field absorption spectroscopy, which highlights the advantage of the NF-tr (NF-abs) method.
(iii) Line-e that also cuts through the 2nd-L produces a more complicated NF-tr energy-location diagram (Fig. 3e). The one-layer (1L) region is similar to that of line-d.
However, once in the 2L region, the coupling between the 1st-L and 2nd-L redshifts the A and In NF-PL, the energy-location diagrams of Fig. 3e' and Fig. 3d' are similar, but they differ in the length of the no-emission region in the middle. Even though the 2nd-L is pure WS2, the interlayer coupling with the bottom alloy layer significantly suppresses its quantum yield to become indiscernible in NF-PL. [24,25] 13 (iv) Line-f cuts through the small multilayer spot in the middle, which exhibits a very strong absorption (Fig. 3f). The rest of Fig. 3f is similar to Fig. 3e While the shifting of the exciton energy generally depends on how layers are stacked [44][45][46], the fact that all A and B excitons in the WS2/MoS2 heterostructure undergo a redshift, as here observed, is somewhat puzzling at first: since the exciton binding scales inversely with the square of the dielectric constant, additional screening due to a second layer should result in a blueshift, instead of a redshift. We then note that the interlayer coupling, in conjunction with the strong spin-orbit coupling in each layer, not only can change the band gap and the band splitting, but also can modify the conduction-electron and valence-hole effective masses, which also enter the exciton binding. The observed redshift for all excitons indicates that these two effects on the conduction and valence band states can overcome the loss of binding due to the additional screening.
The schematics right below Figs. 3c-3g show the vertical layer stackings that correspond to these different lines. However, to delineate the exact boundary between pure TMD and alloy requires further information extracted from the NF-tr images at different photon energies given in Fig. 4, as we now show.
14 In Fig. 4a (same as Fig. 3e), we mark the energy bands associated with various excitons with the same colors used in Fig. 3. The NF-tr images taken at different photon energies are shown in Figs. 4b-4f. The scan of the full energy range is shown in the supplemental videos S2.
The corresponding NF-PL images for three emission energies are shown in Figs. 4d'-4f'. All energy frames feature a strong absorption by the multilayer flake at the triangle center.   In Fig 4d, we see that the WS2-A exciton not only appears in the 1st-L outer area but also in the 2L region. This is yet another evidence that the 2nd-L is pure WS2. The NF-tr profile along the green line marked in Fig. 4b is shown in Fig. 4h, which manifests a 6% absorption drop for each layer at h =2.41 eV.
The identification of pure MoS2 in the alloy region is more challenging. Both the absorption of MoS2-A and MoS2-B excitons cover the whole 2L region (Fig. 4c and Fig. 4e), with a comparatively larger area for MoS2-A. We also note from Fig. 2 that the larger bowing 15 factor for the A exciton makes it less sensitive to the band shifting for a small x value. So, the absorption image of the A exciton is not suitable for distinguishing the edges of the alloy region.
Indeed, the absorption image of the B exciton, shown in Fig. 4c, displays the actual size of pure MoS2 more clearly than Fig. 4e. Moreover, the redshifted band associated with the 1st-L MoS2-A exciton, shown in Fig. 4f, evidences that the coupled area is precisely the same as the shape of the 2nd-L WS2. The light shade at the three triangular corners comes from the MoS2-A band tails of the uncoupled 1st-L.
In Figs. 4d'-4f', NF-PL is prominent in the 1st-L WS2 and 1st-L W-rich alloy regions. But because of the defective MoS2, the NF-PL evolution stops at some x fraction; so, NF-PL images are much less informative than NF-tr images. Note that the PL distribution is not homogeneous since the PL signal is susceptible to local features, such as defects or strains [15,17]. For example, in Fig. 4d', close to the inner edge of the emission pattern, appear many dark spots that mark the locations of the defective MoS2 in the alloy. In the middle, both the defective MoS2 and interlayer coupling lead to an extremely low quantum yield.
With all the above information, we can understand the distribution of composition in the bilayer TMD alloy, as illustrated in Fig. 4g. The boundaries between pure WS2, the WxMo1-xS2 alloy, and pure MoS2 in the 1st-L, and pure WS2 in the 2nd-L can be determined by combining the Nf-tr energy-location diagrams (Fig. 3) and NF-tr images (Fig. 4). Indeed, NF-tr spectral mapping is a powerful technique to study spatially-variant band structures of TMDs and multilayers. It is particularly useful when PL is not available or when the information of the B-exciton is essential.
In conclusion, we used near-field transmittance microscopy to resolve the spatial profile of the complicated WxMo1-xS2 bands associated with the various excitons of MoS2 and WS2.
We have shown that this technique can overcome the problems of chromatic aberration and diffraction limit that plague far-field broadband microscopy. Whereas NF-PL can only measure the A exciton absorption and some monolayer features, NF-tr can moreover detect the B and C 16 exciton absorption features and the composition of multilayer TMDs. This novel technology is here shown to be indispensable for characterizing the lateral distribution and the vertical combination of monolayer and bilayer TMDs.

Sample Preparation.
The WxMo1-xS2 was synthesized by a one-step CVD process. A few-nanometer MoO3 film was first deposited on the sapphire substrate, and WO3 powder was put in a home-built quartz reactor. Both of them were then put in the tube furnace and heated to 900°C. We changed the relative position of the quartz reactor (evaporated WO3) and the substrate to optimize the temperature and reactant supplement for TMD alloys growing. In this way, we could synthesize gradually alloyed interface in the WxMo1-xS2 monolayer. The details of the growth can be found in [39].

NF and FF optical measurements
The NF-tr and NF-PL measurement was performed on the home-built SNOM instrument [47]. A xenon lamp (EQ-99; Energetiq Technology) was used as a white light source with color glass FGS600 to filter the white light spectrum. After fiber coupling, 1.7 mW of broadband light was focused by the first objective lens (50× NA 0.5) into the SNOM tip. Transmitted light was collected by the second objective lens (100× NA 0.9) and guided through a 200-µm fiber into the spectrometer (Kymera-328i, Andor) with a cooling camera (DU420A-BEX2-DD, Andor).
The a-SNOM tips were made of SiO2 hollow-pyramid tips (Nanosensors), and the fabrication processes could be found in [47]. NF-PL was acquired in the same experimental configuration as NF-tr. 6.5 mW of 532 nm DPSS laser was focused into the tip, and emitted PL was accumulated with typically 0.2 second integration time at each pixel. FF-tr was performed under 0.2 mW of broadband illumination on the same homemade SNOM microscope without the SNOM tips.

Calculation of transmittance.
For NF-tr and FF-tr measurements, the transmittance is defined as (x, y) = (x, y)/ (y), where (x, y) are the coordinates for mapping, Is is the sample signal, Iref is the reference signal, which is obtained by averaging the first five data points at the substrate region for each mapping line. In this way, the long-term drift of transmittance can be eliminated. The spectra in Fig. 2c were smoothed with 50 pixels (around 12.5 nm in the spectrum) to achieve better contrast. The band center locations are defined by the location where the differential is equal to 0.

Supporting information
Supplemental Video S1 for FF-tr and NF-tr of the single layer alloy TMD.
Supplemental Video S2 for NF-tr and NF-PL of the bilayer alloy TMD.