Interplay Between Cr Dopants and Vacancy Clustering in the

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Interplay Between Cr Dopants and Vacancy Clustering in the Structural and Optical Properties of WSe2 Ching-Hwa Ho, Wei-Hao Chen, Kwong K. Tiong, Kuei-Yi Lee, Alexandre Gloter, Alberto Zobelli, Odile Stephan, and Luiz Henrique Galvão Tizei ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b05426 • Publication Date (Web): 31 Oct 2017 Downloaded from http://pubs.acs.org on November 1, 2017

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Interplay Between Cr Dopants and Vacancy Clustering in the Structural and Optical Properties of WSe2 Ching-Hwa Ho1,2,* Wei-Hao Chen,1,3 Kwong K. Tiong,3, Kuei-Yi Lee2 Alexandre Gloter4, Alberto Zobelli4, Odile Stephan4 and Luiz Henrique Galvão Tizei4,* 1

Graduate Institute of Applied Science and Technology, National Taiwan University of Science and Technology, Taipei 106, Taiwan

2

Graduate Institute of Electro-Optical Engineering and Department of Electronic and Computer Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan

3

Department of Electrical Engineering, National Taiwan Ocean University, Keelung 202, Taiwan

Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS UMR 8502, F-91405, Orsay, France

4

ABSTRACT Here, we analyze the effect of Cr doping on WSe 2 crystals. The topology and the chemistry of the doped samples have been investigated by atom-resolved STEM microscopy combined with EEL spectroscopy. Cr (measured to have formal valence 3+) occupies W sites (formal valence 4+), indicating a possible hole doping. However, single or double Se vacancies cluster near Cr atoms, leading to an effective electron doping. These defects organization can be explained by the strong binding energy of the CrW—Vse complex obtained by in DFT calculations. In highly Cr-doped samples, a local phase transition from the 2H to the to 1T phase is observed, which has

been

previously

reported

for

other

electron-doped

transition

metal

dichalcogenides. Cr-doped crystals suffers a compressive strain, resulting in an isotropic lattice contraction and in an anisotropic optical bandgap energy shift (25 meV in-plane and 80 meV out-of-plane). Keywords: Transition-metal-dichalcogenide, defects, doping, EELS, STEM, opticalproperties *E-mail: [email protected], [email protected]; 1

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Transition metal dichalcogenides (TMDs)1–3 with composition MX2 (M=Mo, W, Re etc. and X=S, Se) have attracted substantial interest because of their mechanical, chemical, electrical and optical properties. Specifically, they have been used as lubricants, 4,5 as electrodes for photoelectrochemical cells,67 catalysts for sulfur-tolerant hydrogenation and hydrodesulfurization,8,9 field-effect transistors,10,11 flexible electronics,12 polarizationsensitive photodetectors,13,14 light emitters,15 and phototransistors.16 Single-layer WSe217 has been show to contain single photon sources. TMDs with the 2H-phase may be exfoliated into monolayers, which do not have inversion symmetry, enabling carriers valley control in the reciprocal space using light. 18,19 The top of their valence band is constructed from metal d-orbitals, giving rise to strong spin-orbit coupling and spin-split valence bands.19 Valley and spin control opens the possibility to valleytronic and spintronics in the same material.20,21 Production of monolayers is possible because of their layered structure loosely bound by van der Waals forces. This is evident from the easy cleavage perpendicularly to the c-direction, along which 3 atomic layers (X-M-X, where M is a transition metal and X is a chalcogenide) are stacked to form the crystal. Doping 2D TMD semiconductors leads to changes in structural, physical and chemical properties. The presence of Nb-doped WSe2 at interfaces with WxNb1-xSe2 significantly reduces the potential barrier height and improves the performance of the

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corresponding WSe2-based field-effect-transistor devices.22 Mn doping of MoS2 monolayers on sapphire leads to a redshift of ~90 meV of the A-exciton emission. 23 Re doping of WS224 and MoS225–27 results in a transition from a two-layer hexagonal (2H) phase to a three-layer rhombohedral (3R) structure and in a redshift of the A and B excitons. Density functional theory (DFT) calculations indicate that magnetism may be induced on MoS2 by doping with different transition metals.28 An experimental realization of magnetism in TMDs through doping would create a different class of diluted magnetic semiconductors, with applications in spintronic devices.29 In this work, WSe2 single crystals incorporated with various Cr amounts were grown by chemical vapor transport (CVT)30,31 using I2 as transport agent (see Methods section). Millimeter-wide monocrystals (optical images in Figure SI1 in the Supplementary Information, SI) have been characterized using an ensemble of macroscopic and microscopic techniques (Methods) to verify their composition, crystal structure, Cr doping sites and optical band gap. We have observed that substitutional Cr atoms occur at the metal W site, which are systematically accompanied by a single or a double Se vacancy. Even though Cr atoms are in the formal 3+ state, the combination with Se vacancies leads to effective electron doping. Local structural changes between


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the 2H and possibly the 1T phases have been observed in Cr-rich regions, an effect attributed to electron doping.

Results As-produced WSe2 crystals show flat surfaces with step edges, as evidenced by scanning electron microscopy (SEM) images (Figure SI2 in the SI). Five samples with nominal Cr content x=0.00, 0.01, 0.05, 0.10 and 0.20 (x the atomic ratio in the initial mix for crystal production, W1-XCrxSe2) were produced. Qualitative energy dispersive X-ray spectroscopy (EDS) in a SEM indicates that the actual Cr concentration in WSe 2 crystals is much lower than the nominal content. For the x=0.20 sample a concentration of about 2 % was determined, with local fluctuations at scales of tens of micrometers. The presence of Cr in the target material (semiconductor 2H-WSe2) was confirmed by the observation of individual dopant atoms using electron energy loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM) operated at 60 kV. WSe2 bulk crystals are stable in the standard hexagonal 2H phase, as confirmed by X-ray diffraction (XRD) experiments (Figure SI3 in the SI). Moreover, the same structure is observed in atomically-resolved high-angle annular dark field (HAADF) STEM images of exfoliated monolayers (Figure 1(a)). In a first approximation, the HAADF image intensity is proportional to Z 1.6 (see for example Ref. 32). Therefore, in a


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monolayer (Figure 1(a)) W atoms (Z =74) appear with higher intensity than double Se columns (Z = 34). In pure crystals the most common defects observed are single and double Se vacancies, which are shown in Figures 1 (b-c). Simulated and experimental profiles are compared in Figure 1 (d) and simulated images are shown in Figure SI4 of the SI. These defects may be native or created by electron beam irradiation. Single Wvacancies were not observed, while more complicated defects, such as voids, can be created by electron irradiation. This behavior is compatible with previously calculated sputtering thresholds for the acceleration voltage (60 kV) at which experiments were performed.33 WSe2 containing Cr also crystallizes with the 2H-WSe 2 phase, as confirmed by XRD (SI) and HAADF images (Figure 2(a)). In these images darker regions (roughly the size of a single atomic site) are observed in the metal sublattice. As a first guess they could be associated with W vacancies or more complex defects. However, closer inspection at higher magnification shows that these features correspond to W sites occupied by lighter atoms. Spatially resolved EELS permits their identification as individual Cr atoms. The spectrum of a single substitutional Cr atom at a W site (the Cr W defect) is shown in Figure SI5 in the SI, along with the accompanying spectrum image.


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Figure 1. (a) STEM HAADF image of a monolayer region in pure 2H-WSe 2. The circles point to a single (orange) and a double (purple) Se-vacancy, which are shown in detail in (b) and (c). In (b) two single Se-vacancies are seen. (d) Comparison between experimental profiles of a Se-vacancy (orange), a double Se-Vacancy (purple) and of the same defects in simulated images (dashed lines). Simulated images are shown in Figure SI4 of the SI.

The data is shown for a bilayer of WSe2 due to its longer stability under electron beam illumination. EELS data have been analyzed using the HyperSpy Python library.34 In addition to single CrW defects, we have observed more complex defective structures. In Figure 2(a) a distinct cross-like intensity distribution (marked by red


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squares) can be seen. Closer inspection indicates that these features are substitutionalvacancy complexes with a Cr substitutional atom at the metal site and a single or double Se vacancy at a neighboring chalcogen site (Figure 2(b)). In fact, the proximity between CrW and a VSe defects is quite recurrent. On Figure 2(c) a different configuration is shown, where the Se vacancy is located at the third neighbor site in respect to the Cr atom (trans position, atomic structure shown in Figure 3). This attribution is confirmed by comparing profiles without defects (blue), containing a single Se vacancy (green), containing a single substitutional Cr atom (red), and a simulated one containing these two defects (dash line). The Cr (Z = 24) atom can be distinguished from double-Se (2.Z = 68), single-Se (Z = 34) and single-W (Z = 74) columns. The positions of the Cr atom and the single Se vacancy are pointed by dashed red and green circles in Figure 2(c-d). We have observed no experimental evidence pointing to the existence of Cr Se defects in our materials. A spatial correlation between substitutional atoms and chalcogen vacancies has been recently observed in Mo-doped WS2,35 with Mo having the same valence as W atoms (W4+). This clustering of S-vacancies around dopants leads to a possible electron doping (as the MoW-VS complex adds electrons to the conduction band).


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Figure 2. (a) Low-magnification HAADF image of the x=0.10 sample. Darker regions are associated with Cr dopants. Red squares mark positions where a Cr dopant is next to a single or double Se-vacancy. There are three possible orientations for this defect, of which two are observed in (a). (b) High-magnification HAADF image of a Cr/Sevacancy complex. (c) HAADF image of another region of the sample, showing a single Cr atom with a Se-vacancy as a third nearest neighbor (trans site). The positions of the Cr atom and vacancy in (c) can be confirmed in the profiles shown in (d) taken along the colored dashed arrows in (c). The positions of the Cr atom and the Se vacancy are pointed by dashed red and green circles, respectively, in (c) and (d). The intensities for Cr W and VSe are compared to a simulated profile (dashed black line in (d)). The simulated image for this profile is shown in Figure SI4 of the SI.

To obtain further insights on defects clustering we have computed the formation energy of various substitutional-vacancy complexes in the framework of the density


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functional theory. Formation energies have been calculated using chemical potentials corresponding to selenium-rich conditions, a choice justified by the Se excess introduced at the synthesis. According to it, the Se chemical potential has been derived from the Se alpha phase, Cr and W chemical potentials have been obtained considering the most stable selenite forms, Cr2Se3 and WSe2 respectively.1 In Table 1 we report formation energies for a chromium-substitutional defect, an individual selenium vacancy and various substitutional-vacancy complexes for which the position of the Se vacancy in respect to the Cr atom is indicated in Figure 3. We have observed a strong binding energy for all considered substitutional-vacancy complexes, of the order of ~0.5 eV. This tendency corresponds to a lowering of formation energies for V Se close to Cr atoms, explaining the increased abundance of native vacancies for the most Cr doped samples.

EF (eV) CrW

0.55

VSe

3.49

CrW–VSe1st

3.51

CrW –VSe3rd-cis

3.48

CrW—VSe3rd-trans

3.46

CrW—VSe5th-1

3.49

CrW—VSe5th-2

3.50


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Table 1. DFT derived formation energies for a Cr substitutional atom, a Selenium vacancy and various substitutional-vacancy complexes in a WSe 2 monolayer. The atomic configurations used are shown in Figure 3.

Figure 3. Atomic structure configuration for the Cr w–VSe complexes. Experimentally, the complexes with Vse as a first neighbor and a third neighbor on the trans configuration were observed.

In view of these observations, the effective behavior of Cr W atoms in the WSe2 lattice will depend on their valence, which can be formally 2+, 3+ and 6+. XPS measurements (Figure SI3 in the SI) indicate the presence of Cr 3+and Cr6+. In spatially resolved electron energy loss spectroscopy (EELS) the energy position of the L 2,3 edge allows the determination of the CrW valence state.36 For these experiments, we have used Cr2O3 (Cr3+) and K2CrO4 (Cr6+) as references. In all measurements from exfoliated crystals the Cr L3 peak (575.5 eV, Figure 4) is consistently observed at lower energy than those of


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Cr2O3 (577.0 eV) and K2CrO4 (580.0 eV), but higher than those expected for CrSe (574 eV for Cr2+).36 Therefore, the Cr atoms in W sites have a 3+ formal valence. The L 3/L2 intensity ratio is also a possible indication of the valence state, although more sensitive to data noise.36 The XPS result corroborates our valence state assignment. The lower L 2,3 energy compared to Cr3+ in Cr2O3 occurs due to the lower electronegativity of Se (ligand) compared to O. In CrCl3, Cr is also 3+, even though the L3 peak appears at 575 eV.36 Our Cr2O3 and K2CrO4 L3 peak energy measurements are about 1 eV higher than those previously reported in the literature.36

Figure 4. EEL spectra of the x=0.10 and x = 0.20 samples along with those of Cr 2O3 and K2CrO4 measured using the same experimental conditions. The L 3 peaks for Cr in WSe2 samples match the energy position for Cr in the 3+ formal valence state. Spectra have been measured for a large number of Cr atoms by acquiring data while the electron beam was scanning a ~100 nm2-wide area.


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The 3+ formal valence observed would indicate that the Cr substitution at W site leaves extra holes in WSe2, as the W atoms have a 4+ formal valence. However, the systematical observation of single or double Se-vacancies next to these atoms implies an overall electron surplus, a behavior similar to that observed in Mo-doped WS 2.35 In fact, n-doping may be induced by native chalcogen vacancies in pure TMD materials. 37 Cr6+ atoms, only observed in XPS measurements, are probably located in a secondary phase observed in XRD measurements but not in electron microscopy experiments. As the Cr concentration increases, the crystals are progressively more resistant to mechanical exfoliation. In fact, production of wide monolayers of the x = 0.2 crystals was not achieved. Images from Cr-rich regions are consistent with the 1T-WSe 2 phase (Figure 5(a-b)), which can be clearly distinguished from thick 2H phase regions. The 3R phase is also a possible candidate. However, such regions have not been seen in the pure crystals, indicating that the observed images are not related to stacking modification. The 1T phase is metallic. Up to now no 1T-metallic dichalcogenide has been exfoliated into monolayers, possibly explaining the difficulty in cleaving the higher Cr-content samples. The 1T structure association to the images in Figure 5(a-b) is confirmed by image simulations (Figures 5(c)).38 Although the number of Cr atoms cannot be quantified 12 ACS Paragon Plus Environment

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directly from HAADF images of thick specimens, one can infer that the concentration is below the nominal 20 % for the x=0.20 sample, as indicated by EDS. The 1T phase is a minor fraction of the whole volume even in the x=0.20 sample, which explains why it was not observed in the XRD data. The 2H-1T phase transition can be understood in view of our structural and electronic results for the Cr dopants: the Cr 3+ coupled with Se vacancies indicate an electron doping, which is known to promote this phase transition in TMDs.39–41 Electron doping through Li intercalation has also been shown to induce a 2H to 1T transition in MoS2.42 We should note that the stable phase of CrSe 2 is 1T and therefore, apart from purely electronic considerations, a steric effect could contribute in the stabilization of Cr doped 1T-WSe2 domains. The role of multiple and concomitant effects in the 2H to 1T transition has been extensively discussed in Ref.43


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Figure 5. (a) STEM HAADF image of a x=0.20 crystal showing a higher concentration of Cr sites and a different crystal structure, which is shown in detail in (b). (c) HAADF image simulations showing that the contrast observed is consistent with the 1T phase of WSe2. However, a similar intensity distribution is a match to the 3R phase

Along with this microscopic structural change, Cr incorporation influences the global crystal structure. XRD (Figure SI3 in the SI) shows a lattice contraction as a function of Cr nominal content. The decrease is approximately linear with Cr content (Figure 6(a)). The lattice parameters decrease from a=3.297 Å, c=13.024 Å for x= 0.00 to a=3.295 Å, c=13.020 Å for x=0.20. This is consistent with the presence of 1T phase


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domains which have a lattice parameter compression of about 0.6% with respect to the 2H phase as demonstrated by DFT calculations. DFT calculations reported in the literature44,45 also indicate that for small compressive strain (< 1 %) an optical band gap enlargement is expected for WSe2. Lattice contraction influences the macroscopic µRaman and reflectance spectra of doped WSe2 (Figures SI7, SI8 in the SI). Overall, Raman peaks shift to lower energies and become broader, due to lattice disorder (the presence of Cr atoms and secondary phases)

Figure 6. (a) Lattice parameters as a function of Cr content, showing an anisotropic contraction. (b) Energy of transition features observed in reflectance spectra. The out-ofplane transition, C, suffer a much larger shift, indicating a larger optical gap increase.


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Thermo-reflectance (TR) spectra at 20 K and 300 K (Figure SI8 in the SI) show five transition features (denoted A1, A2, B1, B2, and C), which suffer energy blue shift with the increase of the Cr content. This behavior can be explained by a band gap increase caused by the lattice contraction. Interestingly, the effect of contraction on each feature is distinct. Features A1, A2, B1 and B2 suffer a slight blue shift (about 25 meV) while feature C suffers a much larger shift (80 meV). Features A1 and B1 occur due to transitions at the K point (in-plane) with the splitting occurring due to spin-orbit coupling.18 Features A2, and B2 are the second excitonic states (n =2) associated with the first two peaks . Feature C occurs due to transitions at the point which is out-of-plane, implying an anisotropic optical energy gap modification. Overall a 25 meV in-plane and a 80 meV out-of-plane optical energy gap shift was observed.

Conclusion In conclusion, Cr-incorporated WSe2 crystals (nominal contents x=0.00, 0.01, 0.05, 0.10, and 0.20) have been successfully grown by CVT. Pure WSe 2 exists in the two-layer hexagonal (2H) structure, while for Cr-rich samples mixed phases of major 2H and minor (possibly) 1T co-exist, as demonstrated by electron microscopy. This secondary phase exists due to electron doping caused by CrW-Vse complexes. XRD results show that the


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2H-WSe2 phase is compressed as the Cr content increases. This compression results in an anisotropic optical change. Our approach, mixing macroscopic and microscopic techniques, allowed us to understand the lattice compression as a result of a phase change caused by the clustering of Se vacancies around Cr-dopant sites (creating electron doping). Knowledge of the defects atomic structure is imperative for this interpretation. For optoelectronics applications the Cr content may be used to fine tune the optical band gap of WSe2. Finally, the demonstration of the incorporation of transition metal atoms into the 2H-phase indicates the possibility of electronic structure manipulation in 2D semiconductors for applications in valleytronics.

Methods Crystal growth WSe2 single crystals incorporated with various Cr amounts were grown by chemical vapor transport (CVT). This method consists of two steps. First, prior to the crystal growth, a powdered mixture of the starting material were prepared (W: 99.99% pure, Se: 99.999%, and Cr: 99.99%) by reaction at 1050 °C for 10 days in evacuated quartz ampules. To improve the stoichiometry, selenium with 2 mol % in excess was added with respect to the stoichiometric mixture of the constituent elements. About 10 g of this


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mixture was introduced into a quartz ampule (22 mm OD, 17 mm ID, 20 cm length), which was then evacuated to a pressure of 10 -6 Torr and sealed. The mixture was slowly heated to 1050 °C. This slow heating is necessary to avoid any explosions due to the strongly exothermic reaction between elements. In the second step chemical transport was achieved by mixing an appropriate amount of material and transport agent (I2 at 12 mg/cm3) placed in a quartz tube (22mm OD, 17 mm ID, 20 cm length), which was then cooled with liquid nitrogen, evacuated to 10-6 Torr and sealed. The growth temperature was set from 1050 °C to 960 °C with a gradient of -4.5 °C/cm (with crystal growth occurring in the cooler section). The reaction was kept for 480 hours, producing large single crystals. Synthetic Cr-doped WSe 2 single crystals were produced with maximum area up to 1 cm2 (Figure SI1), thicknesses up to hundreds of µm, silver-colored and with mirror-like crystalline surfaces were obtained. Cr-incorporated WSe2 crystals (W1-xCrxSe2,), with different Cr content of x=0.00, 0.01, 0.05, 0.10, and 0.20. (these are the stoichiometric values of the precursors mixed).

Experimental techniques Micro-Raman (μRaman) of the WSe2:Cr crystals were carried out using a RAMaker integrated μRaman–PL system equipped with a 532-nm solid-state diode-pumped laser and a 633-nm He–Ne laser as the excitation sources. A light-guiding microscope (LGM) 18 ACS Paragon Plus Environment

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equipped with an Olympus objective lens (50×, working distance ~8 mm) acts as the interconnection-coupling medium between the sample and the spectrometer equipped with a charge-coupled-device (CCD) camera. A 532-nm laser was used for μRaman experiments. Light reflectance experiments were performed using indirect heating with a goldevaporated quartz plate as the heating element. Heated pulses were generated by a function generator and the heating current was driven by a constant current source. The samples were attached to the heating element by silicone grease. A 150 W tungsten halogen lamp filtered by a PTI 0.2-m monochromator provided the monochromatic light. Incident light was focusing onto the sample with a spot size of about a hundred µm 2. The reflected and scattered light from crystals were collected and detected by a EG&G HUV2000B silicon diode. The signal was detected and recorded via a lock-in amplifier (EG&G model 7265). A RMCmodel 22 closed-cycle cryogenic refrigerator equipped with a model 4075 digital thermometer controller allowed temperature dependent measurements. The XRD samples were prepared from several small crystals of each batch of the Cr-incorporated WSe2 that are finely ground with auxiliary quartz powder. Cu K  radiation was employed and a silicon standard used for calibration.


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XPS measurements were performed in a Scientific K-Alpha system with a monochromatic Al Kα line source. The X-ray spot size in the system can be adjusted to 15−400 μm with an energy resolution of ∼0.02 eV. Experiments were performed on the as-grown c plane of the crystals. An argon ion source facilitates dry etching process of the sample. Due to weak van der Waals bonding between layers along the c-axis allows for exfoliation using razor blade or Scotch tape for mechanical exfoliation or sonication in isopropanol for chemical exfoliation. Atomically-resolved high-angle annular dark field (HAADF) imaging and electron energy loss spectroscopy (EELS) have been performed in a Nion 200 microscope operated at 60 kV, with a convergence semi-angle of 34 mrad and a typical beam current between 20 and 30 pA. EELS experiments were performed using the same microscope configuration, on the same day and ensuring that the energy scale zero (zero-loss peak) was consistently at 0 eV. Cr spectra for monolayers shown in Figure 4(b) have been averaged over long exposures (one spectra every 5 s for a few minutes) with the electron beam scanning a large area (~100 nm2), ensuring an even dose distribution over a large surface . After these averaged measurements the structure was still visibly intact.


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Samples for electron microscopy were prepared by sonication of small TMD crystals in isopropyl alcohol. The as prepared solutions were drop cast in copper grids covered with a carbon film containing holes (known as holey-carbon grids). EDS measurements were performed in a Gemini Zeiss SEM at 30 keV equipped with a Brukker EDS detector. With typical beam current of 20 pA. SEM images were acquired with a secondary electron detector. Electron microscopy data analysis and plotting has been performed with Python 3.0 libraries (Hyperspy, Numpy and Matplotlib) and ImageJ.

Computational method

Density-functional theory calculations have been performed using the OpenMX code. The exchange correlation potential was expressed in the generalized gradient approximation using the Perdew–Burke–Ernzerhof (PBE) schema. We used norm conserving full relativistic pseudo-potentials including a partial core correction and spinorbit coupling. A basis set of optimized numerical pseudo-atomic orbitals was employed.46,47 All defects calculations have been performed considering 6 × 6 ×1 supercells. The in-plane lattice parameter was determined by optimizing the WSe 2


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monolayer and we use a 25 Å c-parameter to reduce interactions between layers in adjacent cells. Structures were relaxed until all forces were less than 10–4 Hartree/bohr.

Image simulations HAADF image simulations have been performed using the QSTEM code. 38 Crystal structures used as input for the calculations have not been relaxed. Parameters were chosen to match our experimental configuration.

■ ACKNOWLEDGMENT This work was financially supported by the Ministry of Science and Technology, Taiwan under the grant No. MOST 104-2112-M-011-002-MY3 and by the National Agency for Research under the program of future investment TEMPOS-CHROMATEM with the reference ANR-10-EQPX-50.

Supporting information The supporting information contains 8 Figures and 1 Table. Figure SI1 and SI2: optical and SEM images of the macroscopic crystals. Figure SI3: XRD data. Figure SI4: Simulated HAADF STEM images.. Figure SI5: Spatially resolved EELS measurements of Cr on WSe2. Figure SI6: XPS data on WSe 2 crystals. Figure SI7: µRaman data and Raman shifts. Figure SI8: Thermo-reflectance spectra at 20 K and 300 K. Table SI1: straight line fitting parameters for the peak shifts in Figure SI8.


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Interplay Between Cr Dopants and Vacancy Clustering in the

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