Sulfur Vacancy Related Optical Transitions in Graded Alloys of MoxW1-xS2 Monolayers

Engineering the electronic bandgap is of utmost importance in diverse domains ranging from information processing and communication technology to sensing and renewable energy applications. Transition metal dichalcogenides (TMDCs) provide an ideal platform for achieving this goal through techniques including alloying, doping, and creating in-plane or out-of-plane heterostructures. Here, we report on the synthesis and characterization of atomically controlled two-dimensional graded alloy of MoxW1-xS2, wherein the center region is Mo rich and gradually transitions towards a higher concentration of W atoms at the edges. This unique alloy structure leads to a continuously tunable bandgap, ranging from 1.85 eV in the center to 1.95 eV at the edges consistent with the larger band gap of WS2 relative to MoS2. Aberration-corrected high-angle annular dark-field scanning transmission electron microscopy showed the presence of sulfur monovacancy, VS, whose concentration varied across the graded MoxW1-xS2 layer as a function of Mo content with the highest value in the Mo rich center region. Optical spectroscopy measurements supported by ab initio calculations reveal a doublet electronic state of VS, which was split due to the spin-orbit interaction, with energy levels close to the conduction band or deep in the band gap depending on whether the vacancy is surrounded by W atoms or Mo atoms. This unique electronic configuration of VS in the alloy gave rise to four spin-allowed optical transitions between the VS levels and the valence bands. Our work highlights the potential of simultaneous defect and optical engineering of novel devices based on these 2D monolayers.


INTRODUCTION
Bandgap engineering is of great importance in modern semiconductor technology because of its capability for tuning the materials' optical and electrical properties that are key to their applications. In the past decade, the emergence of atomically-thin two-dimensional (2D) layered materials have provided an open canvas to engineer their bandgaps for device applications such as tunable lasers, light-emitting diodes (LEDs), and nanoelectronics 1,2 . Among the family of 2D materials [3][4][5] , monolayers of semiconducting transition metal dichalcogenides (TMDCs), such as MoS2 and WSe2 6 , possess direct bandgaps at optical frequencies, making them excellent candidates for bandgap engineering via diverse approaches such as alloying, hetero-stacking, strain engineering, intercalation, temperature control, and applying external electric fields [7][8][9][10][11][12][13][14][15] . Compared to bandgap tuning approaches that rely on external applied factors (e.g., temperature, strain, and electric field), alloying provides an effective and stable control because the bandgap is controlled by the intrinsic chemical composition, and a continuous bandgap engineering can be achieved by precisely modulating the alloy composition 16,17 . To date, ternary alloys of monolayer TMDCs (e.g., MoxW1-xS2, MoS2xSe2(1-x)) have been achieved by means of chemical vapor deposition (CVD) 18,19 , physical vapor deposition (PVD) 20,21 , exfoliation of bulk crystals synthesized by chemical vapor transport (CVT) 22 , and other methods, allowing for the access of tunable optical properties as a function of compositions.
We employed an alkali metal halide-assisted CVD method to synthesize alloyed MoXW1-XS2 monolayers that showcase intriguing compositional gradients within individual crystals, and we thoroughly examined their optical properties. The alloys exhibit distinct compositional gradient transitioning from a Mo-rich center to a W-rich periphery. This strategically controlled alloying within a single crystal enabled the spatial tuning of the bandgap in a wide range (by over 0.1 eV), Additive-assisted CVD has recently emerged as a powerful method for the preparation of 2D TMDCs and their heterostructures 23 .The use of growth additives, such as alkali metal halides (e.g., NaCl, NaBr) and organic compounds with aromatic structures (e.g., reduced graphene oxide (rGO), perylene-3,4,9,10-tetracarboxylic acid tetra potassium salt (PTAS), can effectively promote the growth of TMDCs with enhanced yield, increased grain sizes, and improved uniformity of layer numbers and morphology [24][25][26] . In our work, we employed an additive-assisted synthesis technique to prepare single-crystalline monolayers of alloyed MoxW1-xS2. An alkali metal halideassisted CVD method was applied, with mixed MoS2 and WO3 powders as transition metal precursors and NaBr as a growth promoter (Figure 1(a)). An optical image of typical as-grown MoxW1-xS2 alloys is displayed in Fig. 1(b), showing truncated-triangular morphologies with noticeable optical contrast differences from center to edge regions. Unlike the in-plane heterostructures synthesized by liquid-phase precursor-assisted approach, which we previously reported 27,28 , this method produced alloyed MoxW1-xS2 monolayers with center-to-edge composition gradient (a schematic is shown in Fig. 2(a)), similar to graded TMDC alloys synthesized previously [29][30][31] . Z-contrast aberration-corrected high angle annular dark field scanning transmission electron microscopy (AC-HAADF-STEM) imaging of the MoxW1-xS2 monolayer revealed that the Mo and W concentrations varied continuously from the center to the edge of the flake. The center regions contain a higher Mo concentration compared to the edge regions which are dominated by W with a compositional gradient interface between the two regions. This observation was further confirmed using far-field Raman and photoluminescence (PL) studies as discussed below. AC-HAADF-STEM imaging further identified that VS is the prevalent point defect in alloyed MoxW1-xS2 monolayers, which is labeled by the red-colored circles in Figs. 1(c)-(e). The center, interface, and edge regions contain estimated VS defect densities of 0.185 nm -2 , 0.091 nm -2 , 0.023 nm -2 , respectively. We note that there is a relationship between the prevalent transition metal (Mo or W) and the density of VS. The center, which has the highest Mo concentration, also has the highest density of VS. In contrast, the edge, which has the highest W concentration, has the lowest density of VS. In the interface region, between the center and edge regions, we observed a VS density bounded by the two regions. The VS densities for the Mo-rich center and W-rich edge regions are in accordance with defect densities previously measured in CVD-grown MoS2 and WS2 monolayers 32,33 .

Optical Characterization of alloyed MoXW1-XS2 at room temperature
To characterize the structural and optical properties of as-synthesized TMDC alloys, we performed far-field Raman and PL measurements. and (f). The intensities of both the convoluted WS2 E' and 2LA(M) modes (black line) and the MoS2 E' mode (red line) display a gradual change along the scan direction ( Fig. 2(e)), which unambiguously indicates a composition gradient from center to edge of the flake. Consequently, the optical band gap of the alloyed MoxW1-xS2 was continuously modulated due to the lateral variation of the degree of alloying, indicated by the gradual change in PL peak positions ( Fig. 2(f)) that is consistent with previous results on graded TMDC alloys 29,34 . We also map the band edge emission spatial profile of the MoxW1-xS2 alloy by taking hyperspectral PL imaging 28 . Figure 2(g) shows 3D hyperspectral data cube taken by measuring an array of 75 by 75 pixels PL normalized spectra of the alloyed monolayer. The x and y axes of the 3D data cube shown in Fig. 2(g) indicate the plane of the sample surface while the z-axis corresponds to the photon energy axis (1.85 to 2.0 eV). The acquisition time for each spectrum was 1 sec, and total acquisition time of 2 h per image (see Materials and Methods for details). The PL spatial map at a fixed energy is extracted by crosssection cut of the cube as shown in Fig. 2(h).
The energy dependent PL emission maps reveal 2D quasi-symmetric spatial variation of the degree of alloying from the center to the edge of the flake. In general, the energy gap of an alloy AxB1-x in terms of the pure compound energy gap and , follows an equation 35 Where b is the bowing parameter. For MoXW1-XS2 fitting PL peak positions to the above equation Chen et al. 30 , obtained a b value of 0.25 eV for the A exciton peak and 0.19 eV for the B exciton peak. However, for the alloys AB2(1-x)C2x where both B and C are chalcogen atoms, the bowing was found to be considerably smaller 17 . As the alloy composition is not directly determined in our samples, treating the scan position as a variable, and fitting the PL peaks in Fig. 2(f) to the above equation gives a value of b ~ 0.054 eV suggesting small bowing. From this we surmise that the small bowing parameter indicates small lattice mismatch/strain and thermodynamic miscibility in our samples due to the unique CVD sample synthesis method employed in our study. Low-temperature photoluminescence of the alloyed monolayer MoxW1-xS2 The excitation power dependence of the PL intensities provide insight into the nature of the radiative recombination processes that give rise to the different spectral features near the band edge at different regions of the alloyed structure 36 . To that end we performed laser excitation power-dependent PL spectroscopy at low temperature (T=4 K). Figure 3a shows the PL spectra of

Near band edge peaks (1-3) in the three regions
In order to study the recombination mechanisms of different peaks in different regions of the alloyed MoxW1-xS2 monolayer, we have divided the fitted peaks into two main categories depending on their location relative to the band edges. Firstly, we selected peaks close to the band edges (peaks1-3), then we chose peaks far away from those band edges (peaks 4-6). Figure 3b shows  (Table SI 2), we assign the peaks 1 (~ 2.01 eV) and 2 (~ 1.89 eV) in the Mo-rich side to the B and A excitons, respectively. Similarly, peak 1 in the W-rich side can be assigned to the A exciton. The B exciton in pristine WS2 is generally much weaker than the A exciton and is rarely evidenced 43,44 in PL measurements. Accordingly, by comparing peak 1 in W-rich region (~ 2.01 eV) with the values reported for the A exciton in monolayer WS2 (Table SI 1 peaks by 29 ± 2 meV in region 1, and 36 ± 2 meV and 33 ± 2 meV in regions 2 and 3, respectively. Generally, the PL peak observed on the low energy side of the A exciton in TMDCs is attributed to radiative recombination involving a three-particle (an exciton with an electron or a hole) trion 45,38 , with binding energies in the range 20-40 meV in pristine MoS2 and 40-60 meV in pristine WS2 (Tables SI 1 and SI 2). However, the expected k~ 3/2 dependence on excitation intensity of the assigned trion peak has not been reported 42 . Further, the calculated trion binding energies for MoS2 and WS2 are roughly the same, of the order of 30 meV, and are also very sensitive to the dielectric environment 46 . In an alloyed semiconductor such as MoxW1-xS2, the alloy disorder, if any, may also affect the trion binding energy. As shown in Fig. 3c, peak 3 (region 1) and peak 2 (regions 2 and 3) show k ~ 1 suggesting an excitonic recombination. A previous study in monolayer WS2 assigned the peak on the low energy side, separated by ~ 29-35 meV from the A exciton, to a bound excitonic transition 33 . We conclude that peak 3 (region 1) and peak 2 (regions 2 & 3) are not trion-related transitions but are bound exciton transitions arising from the same impurity or defect in the alloyed MoxW1-xS2. Over the range of excitation powers used, peak 3 in region 2 (~ 1.88 eV) and region 3 (~ 1.93 eV) are separated by 71 ± 2 meV and 69 ± 5 meV, respectively, from the A exciton peak. This peak also shows linear dependence on excitation intensity implying a bound excitonic transition for its origin as well.

Peaks (4-6) far from the band edge in the three regions
As shown in Fig. 3a, the PL spectra from MoxW1-xS2 show significant broadening on the low energy side in all the three regions. The spectral fitting of this region yields three additional peaks, labeled P4, P5 and P6. The dependence of these peaks, observed far from the band edge, on excitation power is shown in Fig. 3d & 3e. The peaks generally show negligible shifts in their positions with increasing excitation power with the exception of peak 5 (~ 1.88 eV @ 1µW; 1.857 eV @ 100 µW) in W-rich side which shows initially a red shift of ~ 20 meV and saturates above 20 µW. It is expected in an alloy semiconductor that upon increasing the excitation intensity the photoexcited carriers migrate to regions of lower bandgap due to compositional grading before recombination. However, since the other peaks do not show such a large red shift, it is likely that peak 5 arises from a localized region of compositional disorder in region 3.

DFT calculations
To assist in the analysis and assignment of the PL transitions observed at low temperature, we

Sulfur vacancy, VS levels (Computational Methods)
The energy levels are all considered at the K point with the distinct energy levels being denoted in the valence band, defect band, and conduction band ( Fig. 4) with W16S31 as an example. In all cases investigated, only the allowed transitions are considered. That is, the energy difference between bands of the same color (blue to blue and red to red) are allowed. The v-c2 and vi-c1   When the VS defect is surrounded by W atoms, the ranges for the defect-mediated transitions match more closely to the P5 and P6 PL peaks observed in the experiment. Defect-mediated transitions associated with the d2 and d3 defect levels are assigned to the P5 and P6 PL peaks across the three distinct regions in Table 1 and Table SI 1 Binding energy is defined as the energy separation of the peak from the A-exciton peak 33 .
A broad band observed at ~ 1.75 eV in monolayer MoS2 similar to the P5 band in Mo-rich region of the alloyed MoxW1-xS2 monolayer in our study has been identified with an exciton bound to ionized donor levels, related to VS 62 . We assign the bands P5 and P6 in region 1 to a free-to-bound transition between the photoexcited electron captured at the VS levels, d3 and d2, respectively and a hole in the valence band. On the other hand, the peaks P3 and P4 in Mo-rich region are identified with recombination through excitons bound to VS levels, d3 and d2, respectively. The peaks P4 in region 2 (MoW side) and P4 & P5 in W-rich region do not correspond to the calculated energy level positions of VS and presumably arise from an unknown defect/impurity. It should be noted that P4 in W-rich side is considerably sharper than P5. Further P4 shows a superlinear dependence on excitation intensity (k > 1) in region 3 while P5 has a sublinear (k < 1) dependence. It may be conjectured that in region 3, P4 and P5 arise from the same defect/impurity with the former being a bound exciton and the latter being a free-to-bound transition. In intermediate MoW region, P4 may be a free-to-bound transition associated with the same defect/impurity. This defect/impurity is introduced as the W content increases.
where Eg(0) is the ground-state transition energy at 0K, S is a dimensionless coupling constant and <ℏω> is an average phonon energy, respectively. Table SI 3  Based on the Fig. 7(b) the red-shift in the peak position of B-exciton in the Mo-rich side is ~ 50 meV when the temperature increases from 4K to 300K which is comparable with reported values 68 . The red shift for A-exciton in all the three regions is about (~33±3 meV) when the temperature increases from 4K to 300K.
The peaks assigned to bound excitons associated with the VS levels d3 and d2 (see Table 1) are generally stable up to room temperature with the exception of the bound exciton associated with the d2 level in region 1 (Mo-rich side) of the alloy which disappears above 100K (Fig.7c). The peaks assigned to an unknown defect with a large exciton binding energy (132 ± 7 meV, Table 1   Compared to the pristine WS2 and MoS2, the changes of the FWHM for A-exciton (X 0 ) in region 1 and region 2 of the monolayer MoxW1-xS2 is larger than the changes of FWHM for pristine samples. For region 1 (Mo-rich side) of the alloy it changes from 70 meV to 120 meV upon increasing the temperature from 4 K to 300 K. However, for the pristine MoS2 FWHM of the Aexciton changes from 38 meV to 50 meV (Fig. SI 15). For the region 3 (W-rich side) of the alloy it changes from 38 meV to 45 meV upon increasing the temperature from 4 K to 300 K (Fig. SI   3). For pristine WS2, the FWHM changes from 45 meV to 52meV (Fig. SI15) which is larger than the reported values for pristine MoS2 70 , and pristine WS2 67 .

CONCLUSION
In summary, using an alkali metal halide-assisted chemical vapor deposition approach, we  SI 1 (b)). Figure SI 1(c) shows the comparison of the FWHM of different spectral peaks (P1-P6) in different regions of the alloyed structure. In general, peaks P4-P6 are broader ( 100 meV) than the band edge transitions P1-P3 ( 60 meV) and the latter are narrower at the edge (W-rich) than at the center (Mo-rich). Peak 4 on the W-rich side which is attributed to a bound exciton due to an unknown defect/impurity shows the narrowest linewidth. (See Table 1    To understand the effect of the alloy on exciton emission and benchmark the alloy spectra, we performed power-dependent PL spectroscopy on pristine MoS2 and WS2 that were grown using identical CVD approach to that of the alloyed ones used above. The experiments were performed at low temperature (T = 4 K) and similar laser excitation parameters (wavelength and power) as in the case of for MoxW1-xS2 were used. Figure SI 9 shows the PL spectra and analysis for both pristine WS2 and MoS2 acquired using excitation laser power from 2 µW to 200 µW. For pristine WS2, the PL spectra were deconvoluted using three pseudo-Voigt spectral shapes. We identify the three peaks with neutral A-exciton (2.04 eV), ( 2 ) dominate the radiative process relative to the intrinsic excitons at low temperature.
Similar dominant low energy transitions that have been observed previously were attributed to excitons bound to defects or impurities. 4,5 . However, in this study, based on the observed sublinear excitation dependence of the peaks, they are assigned to free-to-bound transitions from the doublet VS states.

Power dependence of FHWM for pristine MoS2 and pristine WS2 at T = 4 K
We have plotted the FWHM of different fitted data for both pristine MoS2 and WS2 (Fig. SI 10).
in MoS2. The FWHM of A-exciton is considerably broader than what is reported for exfoliated ML MoS2 6 . The FWHM of A-exciton(~40 meV) for pristine WS2 at low temperature is considerably broader than what has been reported for exfoliated ML WS2 (@ 7K, 18 meV) 6 and also broader than CVD grown WS2 previously reported value of 23 meV at 77K 7 . In both MoS2 and WS2 the broadening can be attributed to inhomogeneous broadening caused perhaps by various factors such as doping, defects, strain, substrate effects.

Temperature dependence of PL for pristine MoS2 and WS2
We also performed temperature-dependent PL spectroscopy of the pristine MoS2 and WS2 samples. The experiments were performed in the temperature range of 4 K to 304 K. Figures  As temperature decreases, the PL peaks show a blueshift. Figure SI 14 (2) shown in the main article. In Table SI 3 are shown the fitting parameters for the A-exciton,

Compilation of peak energies of A-exciton and B-exciton of monolayer WS2 and MoS2.
Optical transitions from monolayer WS2 and MoS2have been rigorously studied by several groups at low temperature as well as room temperature. The observed peak position of A-exciton varies over a wide range from  1.90 eV to 1.96 eV in MoS2 (Tables SI 2) and from  2.01 eV to 2.10 eV in WS2 (Table SI 1). On the low energy side of the A-exciton an optical transition in the range 1.88 eV to 1.92 eV in MoS2 and 1.96 eV to 2.05 eV in WS2 is typically attributed to Atrion. Since the intensity of the optical transition in these above energy ranges show linear dependence on excitation intensity as opposed to a 3 2 ⁄ dependence expected for a three particle trion transition, the involvement of a trion in the radiative process is not unambiguous. It is to be noted that optical transitions on the low energy side of the A-exciton have also been assigned to defect/impurity related bound excitons (See Tables SI 1 and SI 2). In this work we have attributed the low energy transitions to VS defects.  , ( ) = , , 16 31 + (1 − ) , , 16 31 where , 16 31,32 and , 16 31,32 are the transition energies for Mo16S31,32 and W16S31,32, respectively, and similarly , 16 31,32 and , 16   In general, the placement of atoms near VS (or orange position) has the strongest effect with the placement of W atoms tending to increase the defect-mediated transition energies. For all cases regarding the defect-mediated transitions, the presence of W atoms at the pink and black positions tends to decrease the transition energy. For the spin-down (red) transitions, the presence of W atoms at the green and teal positions tends to decrease the transition energies, while for the spinup (blue) transitions, the presence of W atoms at the green and teal positions tends to increase the transition energies. Additionally, the difference between the d2 and d3 energy levels becomes significantly larger when VS is adjacent to W atoms, but when the vacancy is adjacent to Mo atoms, then the difference becomes significantly smaller (Fig. SI 21). Overall, this model predicts the defect-mediated transition energies very well with strong correlation (R 2 = 0.996) with predictions residing very close to the identity line.