Indirect to direct band gap crossover in two-dimensional WS2(1-x)Se2x alloys

In atomically thin transition metal dichalcogenide semiconductors, there is a crossover from indirect to direct bandgap as the thickness drops to one monolayer, which comes with a fast increase of the photoluminescence signal. Here, we show that for different alloy compositions of WS2(1-x)Se2x this trend may be significantly affected by the alloy content and we demonstrate that the sample with the highest Se ratio presents a strongly reduced effect. The highest micro-PL intensity is found for bilayer WS2(1-x)Se2x (x = 0.8) with a decrease of its maximum value by only a factor of 2 when passing from mono- to bi-layer. To better understand this factor and explore the layer-dependent band structure evolution of WS2(1-x)Se2x, we performed a nano-angle resolved photoemission spectroscopy study coupled with first-principles calculations. We find that the high micro-PL value for bilayer WS2(1-x)Se2x (x = 0.8) is due to the overlay of direct and indirect optical transitions. This peculiar high PL intensity in WS2(1-x)Se2x opens the way for spectrally tunable light-emitting devices.


INTRODUCTION
Continuous improvements in the synthesis of two-dimensional materials have enabled the use of these materials in photonics, opto-electronics as well as the emergence of advanced nano-technologies 1,2 . Particularly, transition metal dichalcogenides (TMDs), which possess a high carrier mobility 2 and several interesting spin properties [3][4][5] constitute promising candidates for the study of emergent physical phenomena and functionalities in electronics 5 , photonics and superconductivity 6 . The successful manipulation of these properties makes it possible to exploit the full potential of the TMDs, such as the synthesis of semiconductor alloys with tunable band gaps obtained through the change of chemical compositions [7][8][9][10] and their integration into catalytic 11,12 , opto-electronic and energy related devices 13 . More interestingly, stacked structures of TMDs can improve device performances leading to original device concepts 14 . As examples, multilayer and vdW heterostructures were notably integrated in vertical tunneling FETs and LEDs 15 . The physical characteristics of those 2D materials (bandgap, carrier mobility, doping…) 16 can be tailored by controlling the number of layers (i.e., the thickness) 17,18 , the stoichiometric composition, the strain [19][20][21][22] , the dielectric or electric field environments 23 . There is a very active competitive field, mainly driven by exfoliation, to achieve bilayer or multilayer of 2D material, especially for superconductivity but also for optics. Synthesis techniques such as chemical vapor deposition (CVD) give access to large scale well-controlled bilayer structures with on-demand properties, like a controlled angle between the two lattices. For many reasons, 2D materials, where the optical response remains high in a bilayer or multilayer configurations, are highly sought after.
Furthermore, numerous studies on particular TMDs (MoS 2 , MoSe 2 , WSe 2 , WS 2 ) have revealed that they present a tunable band gap that transits from the indirect to direct band gap when these materials are reduced to a single layer thin film accompanied by a significant improvement in the photoluminescence PL intensity (an increase by one or two order of magnitude) 24 . However, this property which was considered as a common point of all the semiconducting TMDs does not seem to be applicable for certain materials such as MoTe 2 25 . Indeed, recent works have shown that the indirect-to-direct band gap crossover occurs in the MoTe 2 trilayer thus showing that the single and bi-layer being direct bandgap semiconductors. In particular, it was demonstrated that MoTe 2 bilayer still maintains a high PL intensity, which is only 2-3 times weaker than that of the single layer.
In this paper, few-layers of different alloy compositions of WS 2(1-x) Se 2x have been studied in order to uncover the indirect to direct gap crossover as a function of the number of layers. To this purpose, the optical band gap evolution of few-layer alloys was studied using -PL measurements and compared to few thin-layers of WS 2 and WSe 2 . We establish that the measured photoluminescence in WS 2(1-x) Se 2x follows the same trend as that observed in WSe 2 and WS 2 for the alloy compositions where x = 0.3, 0.5 and 0.8. However, the -PL associated to the bilayer thickness for the alloys with higher Se content (x = 0.8) still exhibits a high intensity compared to the monolayer (ML), similarly to thin-layer semiconducting MoTe 2 . To better understand this phenomenon and its origin, the electronic properties have been studied using nano-ARPES and DFT calculations. Our results directly demonstrate the presence of a direct band gap for monolayer alloys and of an indirect band gap for the increasing number of layers. Therefore, the WS 2(1-x) Se 2x alloy monolayer is a direct-gap semiconductor, while the WS 2(1x) Se 2x bilayer presents an overlay of direct and indirect optical transitions. This robustness of PL intensity will ease material integration because it is more tolerant to thickness fluctuation.

Band gap tunability
Using CVD (see the Methods section), we synthesized few-layer WS 2(1-x) Se 2x samples with different chemical compositions (where x = 0.3, 0.5 and 0.8) on SiO 2 /Si substrates 26 . The resulting samples are typically made of single-crystal domains with well-defined hexagonal or triangular shapes 27 . Because WS 2 and WSe 2 share same crystal structure, the random WS 2(1-x) Se 2x alloy can be simply represented as in Fig. 1a where the chalcogen atom site can be either occupied by S or Se (within their relative abundance), without any other distortion or superperiodicity. In Fig. 1b, we show an optical image of a representative flake, identified from its darker optical contrast with respect to the underlying substrate, exhibiting an equilateral triangle shape.
To study the band gap tunability associated to the modification of the S/Se stoichiometric ratio in the WSSe layer 28 , we performed μ-PL measurements, using a confocal microscope setup 29 . We recorded PL spectra for each alloy on mono-, bi-and tri-layer (1, 2 and 3 ML) thick flakes, which we compared to the ones of pure WS 2 and WSe 2 samples. As shown in Fig. 1c and Supplementary Fig. 1, the PL spectral peaks of the single-layer  Similar attenuated drop of the maximum PL intensity by only a factor of 2 when passing from mono-to bi-layer of WS 2(1-x) Se 2x (x = 0.8), can be traced on two distinct flakes presenting 2H and 3R stackings 32 . In Fig. 2a, e, we present the optical images, obtained from a triangular and another hexagonal flake. The change in contrast represents different thicknesses of the flake. Their corresponding PL intensity and peak position maps are reported in Fig. 2b, c for the triangular flake and in Fig. 2f, g for the hexagonal one, respectively. The changing in the intensity contrast in the PL intensity maps confirms that the number of layers varies across each flake: a higher intensity scale actually indicates a decrease in the number of layers and vice versa 29 . This is also proved by taking punctual PL spectra in each region of each flake, see Fig. 2d, h. By comparing the spectra of Fig. 2d, h to the ones of Supplementary Fig. 2e, obtained from another sample with the same S/Se stoichiometric ratio, we find a high degree of reproducibility of our results. Thus, the observed peculiar behavior of the sample with the Se content at 80% does not depend on the shape of the flake or on its stacking order 16   shows three μ-XPS spectra of the Se 3d (W 4f, respectively) core level acquired on three distinct points of each region. The experimental data points are represented as black, red and blue circles, the Voigt envelop of fitted components is shown as a green solid line, and the fitting components are plotted as orange and blue curves 30 .
All the Se 3d spectra consist of a single pair of spin-orbit doublet, corresponding to Se 3d 5/2 and Se 3d 3/2 and attributed to the bonding with W (spin-orbit splitting of 0.83 eV, 3d 3/2 :3d 5/2 ratio of 0.6, and FWHM of 0.5 eV).
The W 4f spectra (Fig. 3c), on the other hand, can be well fitted by two pair of spin-orbit doublets, corresponding to W 4f 5/2 and W 4f 7/2 and relative to the bonding with the two chalcogen atoms S and Se (spin-orbit splitting of These photoemission spectra are used to estimate the Se contents of the WSSe alloys. The total amount of Se atoms is calculated from the Se 3d and W 4f peak area ratio in the surface sensitive configuration, weighted by their relative cross sections. In order to unambiguously evaluate the direct or indirect bandgap character of the 1ML, 2ML and 3ML of WS 2(1- x) Se 2x (x = 0.8), we investigated the electronic band structure of this alloy crystal experimentally by means of ARPES and theoretically with DFT calculations 42,43 . Figures 4a-c present the photoemission intensity maps acquired at 100 eV on mono, biand tri-layers of WS 2(1-x) Se 2x (x = 0.8), respectively along the Γ-K direction 44 .
Their second derivatives on which the theory (blue dashed lines) is overplotted are instead reported in Fig. 4d-f.
The top of the valence band at the K point is mostly formed by planar d xy and d x2-y2 orbitals of tungsten, while at the  point the band is mostly composed by W d z orbitals and S, Se p z orbitals based on DFT calculations 30 .
Because of their out-of-plane character, the bands with the lowest energy at  are the most sensitive to the number of layers composing the system and, as shown in Fig. 4, the single down-dispersing parabola of the 1ML splits into two (three) parabolas for 2ML (3ML) 45 . This detailed evolution of the valence band structure for different WS 2(1-x) Se 2x (x = 0.8) thicknesses is highly useful in terms of offering a direct way to determine the , bi-and tri-layer WSSe, respectively, which represent high values compared to other 2D materials 45 . Besides, the energy difference between the K and Γ points (E K − E Γ ) is about 500 meV, -60 meV and -480 meV for mono-, bi-and tri-layer WSSe, respectively. A similar trend was already observed for few layer WSe 2 by Y.
Zhang et al. 46 In their case, the energy difference between the K and Γ points at the VBM (E K − E Γ ) was about 560 meV, -80 meV and -11 meV for mono-, bi-and tri-layer WSe 2 , respectively. For bi-layer WS 2(1-x) Se 2x (x = 0.8), the fact that the top of the VB at K point is slightly lower than the one at Γ suggests that 2 ML of WS 2(1-  In summary, we have successfully studied the electronic properties of different thicknesses of WS 2(1-x) Se 2x alloys with tunable content on sulfur and selenium. We demonstrated that the PL intensity increases when the number of layer decreases. Remarkably, we found that for the high Se content, WS 2(1-x) Se 2x (x = 0.8) exhibits an atypical behavior when the number of layers is reduced. For this particular composition, we observe a high PL signal for both monolayer and bilayer with a drop of the maximum intensity by only a factor 2 when switching from monoto bilayers. This is interpreted as the signature of the presence of competing contributions of direct and indirect optical transitions, which was confirmed experimentally by ARPES and theoretically by means of DFT calculations. Consequently, by changing the alloy content and the thickness, one can achieve spectrally tunable and robust electroluminescent devices.

METHODS
Growth of WS 2(1-x) Se 2x /SiO 2 /Si(001): WS 2(1-x) Se 2x samples were grown by chemical vapor deposition (CVD) in a 1" quartz tube furnace. A quartz boat contained WS 2 and WSe 2 powder was loaded at the center of the furnace.
SiO 2 /Si substrate was placed at the downstream of the furnace. Before heating, an Ar gas flow was introduced into the system for 10 min in order to exhaust the air and maintain the flow at 70 standard-state cubic centimeter per minute (sccm). The furnace was then rapidly heated to 1100 °C in 30 min. After keeping the growth at this temperature for 5 minutes, the furnace was then cooled down to room temperature naturally.

µ-PL measurements:
The µ-PL measurements were conducted at room temperature, using a commercial confocal Horiba micro-Raman microscope with a 100× objective and a 532 nm laser excitation. The laser beam was focused onto a small spot having a diameter of ~1 μm on the sample and its incident power was about 5 μW.
All measurements are acquired with a 532 nm laser excitation at room temperature.
Band structure of few layers WS 2(1-x) Se 2x : The ARPES measurements were conducted at the ANTARES beamline of Synchrotron SOLEIL (Saint-Aubin, France). We used linearly horizontal polarized photons of 100 eV and a hemispherical electron analyzer with vertically-confining entrance slit to allow band mapping. The total angle and energy resolutions were 0.25° and 10 meV. All nano-XPS/ARPES experiments were done at low temperature (70 K).
Theoretical calculations: we performed plane-wave density functional theory (DFT) simulations by means of the Quantum EPSRESSO code 48 . To include the spin-orbit interaction, we realized noncollinear calculations with the adoption of fully relativistic norm-conserving pseudopotentials. In order to attain a better estimation of the band gap, we adopted the HSE hybrid functional 49 to approximate the exchange-correlation term. The selfconsistent solution was obtained by using a 15x15x1 Monkhorst-Pack k-points grid centered around the Γ point and a cutoff energy of 50 Ry. In layered materials, the van der Waals forces were accounted by means of the semiempirical Grimme DFT-D3 correction 50 . A vacuum space of 24 Å in the z direction was assumed in the unit cell to suppress the interaction between two adjacent sheets in the periodic arrangement. The cell parameters and atomic coordinates were fully relaxed by using a convergence threshold for forces and energy of 10 -3 and 10 -4 (a.u,), respectively. The WSSe was simulated within the virtual crystal approximation (VCA), where at each chalcogen position we located a virtual atom whose pseudopotential is given by a linear interpolation of the pseudopotentials for S and Se. Such a mean-field approximation is expected to provide the correct trends of the band-structure evolution of samples with sufficiently large surfaces.

DATA AVAILABILITY
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.