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Evolution of Electronic Structure in Atomically Thin Sheets of WS2 and WSe2

Geometrical confinement effect in exfoliated sheets of layered materials leads to significant evolution of energy dispersion with decreasing layer thickness. Molybdenum disulphide (MoS2) was recently found to exhibit indirect to direct gap transition when the thickness is reduced to a single monolayer. This leads to remarkable enhancement in the photoluminescence efficiency, which opens up new opportunities for the optoelectronic applications of the material. Here we report differential reflectance and photoluminescence (PL) spectra of mono- to few-layer WS2 and WSe2 that indicate that the band structure of these materials undergoes similar indirect to direct transition when thinned to a single monolayer. Strong enhancement in PL quantum yield is observed for monoayer WS2 and WSe2 due to exciton recombination at the direct band edge. In contrast to natural MoS2 crystals extensively used in recent studies, few-layer WS2 and WSe2 show comparatively strong indirect gap emission along with distinct direct gap hot electron emission, suggesting high quality of synthetic crystals prepared by chemical vapor transport method. Fine absorption and emission features and their thickness dependence suggest strong effect of Se p-orbitals on the d electron band structure as well as interlayer coupling in WSe2.

Atomically thin sheets of MoS 2 consisting of a single to a few monolayers were recently found to exhibit a set of unusual properties associated with its two dimensional (2D) structure and high crystal quality, triggering significant research interest. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] Similar to graphite, MoS 2 crystallizes in a van der Waals layered structure where each layer consists of a slab of S-Mo-S sandwich. Individual monolayers can be mechanically peeled off from a bulk crystal and isolated as graphene-like 2D crystal. 19 While MoS 2 is traditionally known as solid-state lubricant and catalyst, its monolayer crystal hold promise in novel electronic and optoelectronic applications as well as provide access to fundamental physical phenomena.
Electronically, a bulk MoS 2 is an indirect gap semiconductor with the bandgap in the nearinfrared frequency range (~ 1.2 eV). 20 In contrast, monolayer MoS 2 is a direct gap semiconductor with the band gap in the visible frequency range (~ 1.9 eV). [4][5] Confinement of carriers in the out-of-plane direction induces gradual increase in the band gap with decreasing thickness. 21 The indirect to direct crossover occurs at the monolayer limit resulting in strong contrast in photoluminescence (PL) efficiency between single and multilayer sheets. [4][5] Remarkable electrical properties of mono-and few-layer MoS 2 are increasingly revealed in its field effect transistor characteristics such as exceptionally large on/off ratio, small subthreshold swing, ultra-low off-state energy dissipation, high field effect mobility, and large current carrying capacity. [1][2][3] Explicit inversion symmetry breaking in monolayers allows valley selective pumping of charges using circularly polarized light. [6][7][8] High electronic quality of the material coupled with thickness dependent optical properties, mechanical flexibility, 9 and access to valley degree of freedom highlights some of the distinct characteristics of atomically thin MoS 2 . [10][11][12][13][14][15][16][17][18] Tungsten-based dichalcogenides such as WS 2 and WSe 2 belong to the same family of layered transition metal dichalcogenides (LTMD) as MoS 2 . 22 Mechanically exfoliated atomically thin sheets of WS 2 and WSe 2 were recently shown to exhibit high in-plane carrier mobility and electrostatic modulation of conductance similar to MoS 2 . [23][24] Both compounds exhibit trigonal prismatic structure and are indirect gap semiconductors in the bulk form with a bandgap of ~ 1 eV as MoS 2 . The lattice constants are nearly identical for MoS 2 (3.16 Å) and WS 2 (3.15 Å) while WSe 2 exhibits a slightly larger value (3.28 Å). 22 Interlayer distance is correspondingly larger for WSe 2 due to the large size of Se atom. General features of the WS 2 and WSe 2 band structures are similar to those of MoS 2 where a direct and indirect gap coexist irrespective of thickness. [25][26][27] Direct gap exists at the K points of the Brilloun zone between spin-orbit split valence band and doubly degenerate conduction band. On the other hand, indirect gap forms between a local conduction band minimum at a midpoint between Γ and K and valence band maximum at the Γ point. The primary difference between MoX 2 (where X represents chalcogen atoms) and WX 2 is the size of the spin-orbit splitting due to the different size of the transition metal atom.
While MoS 2 2D crystals have been extensively studied recently, understanding of confinement effects on WS 2 and WSe 2 in the mono-to few-layer thickness regimes is limited.
Here we report the evolution of optical absorption and PL spectra of mechanically exfoliated sheets of synthetic 2H-WS 2 and 2H-WSe 2 with thicknesses ranging betweeen 1 and 5 monolayers. The excitonic absorption and emission bands were found to gradually blueshift with decreasing number of layers due to geometrical confinement of excitons. Strong enhancement in PL efficiency is observed in monolayers indicating that they are direct gap semiconductors in agreement with the recent experimental findings [28][29] and calculations. [25][26] We show that interlayer coupling effects can be investigated by studying fine absorption and emission features and their dependence on sample thickness. We further demonstrate that the PL emission efficiency of monolayers is higher for synthetic WS 2 and WSe 2 crystals compared to natural MoS 2 crystals.

Results/Discussion
Mechanically exfoliated flakes of WS 2 and WSe 2 were deposited on quartz or SiO 2 /Si substrates and their thickness was verified by atomic force microscopy (AFM) and optical contrast (See Supporting Information for AFM images). 30 These samples were chemically stable over 3 months in ambient conditions and showed no obvious sign of degradation according to our Raman analysis. 31 For atomically thin layers suppoted by a transparent substrate, differential reflectance provides an effective measure of absorbance. Fractional change in reflectance δR for a thin layer sample relative to the reflectance of a dielectric substrate with refractive index of n subs is related to the absorbance (A) of the material by 32 (1) We assume n subs to be wavelength independent for the spectral range investigated in this study. Figures 1a and 1b show the differential reflectance spectra of 1-5 layer WS 2 and WSe 2 , respectively. Absorption features for bulk crystals have been previously studied by Beal et al. 33 and Bromley et al. 34 General features of the peaks are in good agreement with previously reported results. All peaks exhibit gradual but distinct blueshift with decreasing sample thickness similar to early findings. 35 Excitonic absorption peaks A and B which arise from direct gap transitions at the K point are found, respectively, around 625 nm and 550 nm for WS 2 and around 760 nm and 600 nm for WSe 2 in agreement with the previous studies on bulk layers. [33][34] The energy difference between the A and B peaks, which is an indication of the strength of spin-orbit interaction, is approximately 400 meV for both WS 2 and WSe 2 in reasonable agreement with the calculations. 36 It should be noted that this value is significantly larger than the ~160 meV splitting observed for MoS 2 . [4][5] For WS 2 , an additional peak, previously labeled as C, is observed around 450 nm. This peak arises from optical transitions between the density of states peaks in the valence and conduction bands. 37 The WSe 2 spectra show more additional features due to greater overlap of anion p orbitals with tungsten d orbitals as well as those of adjacent layers. [33][34] The absorption peaks A' and B' are believed to be excitonic in nature and arise from splitting of the ground and excited states of A and B transitions, respectively, due to inter-and intralayer perturbation to the d electron band by the Se p orbitals. [33][34] The energy separation between A' and B' peaks are found to be ~ 400 meV consistent with this picture. It may be noted that the presence of A' and B' peaks in monolayer WSe 2 suggests that A-A' and B-B' splitting are mainly due to intralayer effects.
In contrast to absorption, PL spectra show remarkable dependence on sample thickness for both materials as shown in Figure 2a   indication of interfacial quality. 38 A recent study showed that the size of Stokes shift in monolayer MoS 2 increases with doping concentration. 39 The narrow emission line, whose FWHM is comparable to thermal energy at room temperature, along with the small Stokes shift indicates high quality of our WSe 2 samples.
In addition to the A exciton peak, another peak at a longer wavelength was observed for multilayer samples of both materials. This is attributed to indirect band gap emission involving condution band minimum at a midpoint between K and Γ points and valence band maximum at the Γ point. Calculations show that for WSe 2 bilayers, the indirect gap emission involves valence band maximum at the K point which is nearly degenerate with the band maximum at the Γ point. 26,40 It should be noted that the indirect gap emisision peak is virtually absent in the monolayer emission spectra, indicating that both WS 2 and WSe 2 become a direct gap semiconductor when they are thinned to a single monolayer. This observation along with the distinctly strong emission from monolayers is in good agreement with the calculated 25-27 results as well as very recent experimental findings. 28 We observed that the decay in emission intensity with increasing thickness is more moderate for WSe 2 compared to WS 2 . This is attributed to the small difference between the direct and indirect emission energies. For bulk WSe 2 , the energy difference between the Γ and K points of the valence band was previously measured by photoemission spectroscopy to be < 80 meV. [41][42] Theoritical calculations also yield similar results 26,40 . For bilayer WSe 2 , the difference between the direct and indirect gaps is a measure of the energy separation between the conduction minimum at the K point and at a midpoint between Γ and K points.
Based on our PL results we find this energy seperation in bilayer WSe 2 to be about 70 meV.
In comparison, the difference between the indirect and direct band gaps in bilayer WS 2 is much greater (~ 300 meV). Because the population of hot electrons that transiently occupy the direct band edge at the K point is higher in bilayer WSe 2 due to the smaller energy difference between its direct and indirect gaps, its A exciton hot electron emission is pronounced. A similar scenario was recently reported for few-layer MoSe 2 . 43 For multilayer samples, the indirect gap emission intensity is comparable to or higher than that of hot electron emission from A excitons. We compared the indirect gap emission intensity of commercially available natural MoS 2 and our tungsten dichalcogenides grown by CVT and found that the emission intensity was distinctly higher for synthetic WS 2 and WSe 2 .
Radiative recombination across an indirect gap is a slow process requiring phonons with an appropriate momentum. In the presence of defects acting as nonradiative traps, nonradiative decay will dominate and suppress the PL QY. Observation of comapratively strong indirect gap emission therefore provides further evidence that our CVT-grown samples are of high quality. and WSe 2 is 20 to 40 times higher than that of monolayer MoS 2 obtained from a natural crystal. The emission from bilayer WSe 2 is also more efficient in comparison to monolayer MoS 2 . The differences in PL QY may arise due to various intrinsic and extrinsic factors.
Doping is expected to play a major role in suppressing PL in monolayers. [44][45] Since the materials studied here are unintentionally doped at different concentrations, we suspect that the observed differences mainly arise from doping. Further studies are required to elucidate the origin of the variation in PL QY reported here.

Conclusions
In summary, we studied the evolution of electronic structure in atomically thin WS 2 and WSe 2 sheets using differential reflectance and PL spectroscopy. Our results demonstrate that indirect to direct crossover occurs in these materials when they are thinned to a single         spectra are equivalent to the differential reflectance spectra presented in the main text. The spectra are normalized and overlaid for clarity.