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Resonant Raman and Exciton Coupling in HighQuality Single Crystals of Atomically-Thin Molybdenum Diselenide Grown by Vapor Phase Chalcogenization Ismail Bilgin, Aldo S. Raeliarijaona, Michael C. Lucking, Sebastian Cooper Hodge, Aditya D. Mohite, Andres de Luna Bugallo, Humberto Terrones, and Swastik Kar ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b07933 • Publication Date (Web): 27 Dec 2017 Downloaded from http://pubs.acs.org on December 27, 2017

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Resonant Raman and Exciton Coupling in HighQuality Single Crystals of Atomically-Thin Molybdenum Diselenide Grown by Vapor Phase Chalcogenization Ismail Bilgin,1 Aldo S. Raeliarijaona,2 Michael C. Lucking2, Sebastian Cooper Hodge1, Aditya D. Mohite3, Andres de Luna Bugallo,1,4,* Humberto Terrones,2,** Swastik Kar,1,*** 1

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Department of Physics, Northeastern University, Boston, MA, USA

Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, NY USA 3

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Los Alamos National Laboratory, Los Alamos, NM USA

CONACYT - Cinvestav Unidad Querétaro, Querétaro, Qro. 76230, Mexico

ABSTRACT

We report a detailed investigation on Raman spectroscopy in vapor-phase chalcogenization (VPC) grown, high-quality single-crystal atomically-thin molybdenum diselenide samples. Measurements were performed in samples with four different incident laser excitation energies

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ranging from 1.95 eV < Eph < 2.71 eV, revealing rich spectral information in samples ranging from N=1-4 layers and a thick, bulk sample. In addition to previously observed (and identified) peaks, we specifically investigate the origin of a peak near ω≈250 cm-1. Our density functional theory (DFT) and Bethe-Salpeter (BSE) calculations suggests that this peak arises from a doubleresonant Raman process involving the ZA acoustic phonon perpendicular to the layer. This mode appears prominently in freshly-prepared samples and disappears in aged samples, thereby offering a method for ascertaining the high optoelectronic quality of freshly-prepared 2D-MoSe2 crystals. We further present an in-depth investigation of the energy-dependent variation of the position of this and other peaks and provide evidence of C-exciton-phonon coupling in monolayer MoSe2. Finally, we show how the signature peak positions and intensities vary as a function of layer-thickness in these samples.

Corresponding Authors: * [email protected] **[email protected] ***[email protected] TABLE OF CONTENT GRAPHIC


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Atomically-thin layered (2D) materials such as graphene, transition metal dichalcogenides, and a range of other layered compounds1 remain some of the most interesting systems for exploring a wide range of electronic,2 excitonic,3 valley,4 and correlated5 physics in two-dimensional (2D) confinement. While carriers in graphene demonstrate massless Dirac Fermionic behavior,6,7 unusual half-integer quantum Hall effect,8 field-tunable electron-phonon coupling9 and fieldtunable plasmons,10,11 other 2D systems have shown tunable valley magnetic moments12,13 and excitons,14,15 appearance of gate-tunable superconductivity,5 spin-Hall

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and valley-Hall

effects,17 and tunable many-body physics18 in 2D materials beyond graphene.19-22 In addition to their fundamental properties, these materials possess enormous potentials for transistors23 and photonic devices,24 nanoelectronics,25 optoelectronics,26 photodetection,27,28 memory,29 and energy technologies30. Both from fundamental as well as applications perspectives, a key issue of primary importance is the development of reproducibly-synthesizable 2D materials of high crystalline quality, ascertaining which requires investigations at various size-scales. At the atomic scale, both TEM31-33 and STM34,35 have been used as a high-fidelity tool to investigate the defect, impurities, and grain boundary properties of these materials, as these are expected to have a significant impact on transport and mechanical properties of 2D materials.36,37 However, such probes are extremely localized to a few-hundred-atoms scale, and it is laborious and experimentally untenable to scan the overall impact of these disorders on the properties of larger-area, micronsscale samples. At these size-scales, their carrier mobility has often been used as a measure of material quality,38,39 since mobility is a direct measure of the impact of various scattering mechanisms within the material. However, mobility measurement involves introduction of contacts (which can easily dope samples, form imperfect junctions, and adversely affect the


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measured mobility), and performance of lithography (which introduces impurities from various polymeric resists, solvents etc.). Another technique – i.e. Raman spectroscopy, has remained an alternate, non-invasive and highly sensitive probe to investigate both novel physics as well as sample-quality of 2D materials.40-42 It has been long established, well before the onset of research in 2D materials, that Raman spectroscopy is one of the most powerful techniques for characterizing nanomaterials.43 This technique probes the three major contributors to their electronic properties, i.e. carriers, photons, and phonons.42 In addition, Raman spectroscopy is also highly sensitive to various other aspects that have a strong impact on the electronic and optical properties of 2D materials, such as layer-thickness, substrate-dependence, strain, and defects, to name a few.41,44,45 In this work, we report on the synthesis of high-quality 2D-MoSe2 using a vapor-phase chalcogenization (VPC) – a modified chemical vapor deposition (CVD) process – and their detailed characterization using Raman spectroscopy. The obtained Raman active modes have been discussed in the framework of the electronic structure and vibrational dispersion modes using first-principles density functional theory (DFT). Unlike 2D-MoS2, which has been extensively investigated for its fundamental properties as well as application potentials, 2DMoSe2 has received far less attention. A range of recent works have revealed a great deal about the vibrational modes that lead to Raman spectroscopic peaks in MoSe2. Some of the most detailed investigations of Raman spectra have been reported in either bulk or mechanicallyexfoliated samples of MoSe2, since it is widely accepted that such samples have higher electronic quality. Nam et al., performed detailed Raman spectroscopic investigation bulk commercial MoSe2, documenting and investigating the evolution of the most prominent peaks as a function of excitation energy.46 Soubelet et al. extended this work by investigating layer-thickness


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dependent and excitation-energy dependent Raman on 2D-MoSe2 obtained from mechanicallyexfoliated samples.47 Similar mechanically-exfoliated samples were used by Chen et al. to reveal the effect of optical helicity-dependent Raman scattering in 2D-MoSe2,48 and by Kioseoglou et al., who investigated inter-valley scattering through Raman studies.49 In addition, detailed studies of low-energy modes have been performed on (CVD)-grown MoSe2 samples, for example, by O’Brien et al., who measured and mapped these modes40,50 and by Lu et al. who investigated the effect of stacking sequence and polymorphism on Raman spectra51. However, their data do not appear to reveal several intermediate- and high-energy fine structures present in the 2D-MoSe2 Raman spectrum. Other reports utilize Raman spectroscopy as a tool to identify/characterize MoSe2 in a number of CVD-synthesis works, including pure phase 2D-MoSe2, and its alloy and heterostructures with 2D-MoS2,52-57 by identifying their signature A1g and E12g modes. A survey of these works appears to indicate that some of the detailed fine structures in Raman spectra have so far remained challenging to observe in CVDgrown MoSe2, very likely due to their lower quality compared to the mechanically-exfoliated counterparts. In the field of 2D materials, this reflects an important issue, since development of applications will require low-cost, scalable methods such as CVD to match sample quality that is comparable to that of mechanical exfoliation. In an earlier work, we had addressed this issue for another 2D material, i.e. 2D-MoS2 58. In conventional CVD, TMDs can be grown using a MoO3 precursor, where MoO3 is first reduced to form MoO3-x, followed by its sulfurization to MoS2. We had argued that this two-step process could lead to incomplete reactions and mixed-phase formation of MoS2 and MoO2. This, and the increased possibility of oxygen-impurity doping in the samples could reduce the crystallographic integrity and functional behavior of atomically thin MoS2. In its place, a single-step, oxygen-


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reduced reaction using MoO2 as the precursor would allow efficient chalcogenization in the vapor phase prior to crystallization of MoS2 on a substrate, which we argued would lead to better crystalline quality of the sample. We had supported this conjecture by demonstrating superior electronic and optoelectronic properties in vapor-phase-sulfurization-synthesized MoS2 (with MoO2 as the precursor), including the demonstration of high carrier mobility and FET ON/OFF ratio comparable to those obtained in exfoliated samples, a rich range of Raman active modes including unreported Raman-peaks, and detailed characterization of excitonic processes using photocurrent spectroscopy. In particular, Raman spectroscopy not only established their high sample quality, but also enabled us to demonstrate additional vibrational modes in single- and few-layered VPC-grown MoS2. Since Raman spectroscopic peaks involve complex photonelectron-phonon and photon-exciton-phonon (including resonance, second-order, and defectinduced) processes, they are far more susceptible to poor sample quality than, for example, mobility measurements (which are mostly confined to near-Fermi level processes, and do not involve photons and higher-order interactions). Hence, we believe that obtaining high-quality fine-structure Raman spectra is perhaps a more powerful tool for ascertaining quality of 2D materials. Indeed, the high quality of samples synthesized using as-grown VPC enabled us to reveal detailed bias-dependent exciton dynamics that was previously obtainable only in suspended, annealed mechanically-exfoliated samples.58 In this work, we have extended the efficacy of our MoO2 – based VPC method, to synthesize high-quality 2D-MoSe2 samples. We present extensive excitation-energy and layer-thickness dependent Raman spectroscopy of these samples that establishes their high quality. In particular, we study the nature of the peak ~250 cm-1 in monolayer samples in conjunction with firstprinciples calculations. Density Functional Perturbation Theory (DFPT), the application of the


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Fermi golden rule and BSE calculations lead us to propose that this peak, whose origin has not been previously discussed, arises from a double resonant Raman process involving the acoustical out of plane phonon ZA(M) in a similar fashion as the LA(M) mode in WS2 59. In addition, we present several other previously unreported energy- and layer-thickness-dependent features of the 2D-MoSe2 Raman spectra, which provide deeper insights into their spectral behavior.

RESULTS AND DISCUSSIONS Large area high quality single and few-layer MoSe2 flakes were synthesized using MoO2 (molybdenum dioxide) and selenium powder in a quartz-tube-in-a-furnace vapor-phased deposition system similar to the one described in our earlier work.58 Figure 1a-c and 1d show optical and SEM images, respectively, of typical VPC-grown monolayer flakes of MoSe2, a large number of whose edge-lengths varied approximately between 10 microns to 100 microns. Similar samples could also be grown in quartz substrates, as shown in the optical image of figure 1c. The samples mostly had clear geometrical symmetry, indicating their single-crystal nature, although in some cases, polycrystalline samples with merged geometry or with grain boundaries were also found.


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Figure 1. Optical images of typical VPC-grown single-layer MoSe2 on (a-b) Si/SiO2 and (c) quartz substrates, highlighting various sizes and morphologies. (d) Typical SEM image of single layer MoSe2 on Si/SiO2 substrates. (e) Typical AFM topographical image (scale bar = 5 microns) of a monolayer MoSe2 sample, its thickness ≈0.8nm determined from the stepheight as shown in the the height profile (inset) along the white line in AFM image. (f) Typical Photoluminescence spectrum of single-, few-layered and thick MoSe2 samples.

The shapes of the flakes were found to be sensitive to the hydrogen concentration during growth, and could be tuned from triangular to hexagonal shapes by increasing hydrogen concentration in Argon (from 1%-4%)) in a manner reported previously for CVD synthesis of 2D-WSe2.60 Figure 1e depicts an AFM image of monolayer MoSe2 grown on SiO2/Si substrate, the measured step height obtained from the (step-height line section shown in white) is about 0.8 nm, which compares well with the previously-reported sample thickness of single-layer MoSe2 54,55

. Figure 1f shows the layer-thickness-dependent photoluminescence spectra in the samples.


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The direct-gap single-layered sample demonstrates the characteristic strong peak at 1.51 eV originating from the A-exciton, and a second shallow feature near 1.71 eV originating from the B-excitons. Peaks observed from samples with greater thicknesses were rapidly quenched, due the well-known transition of the systems from a direct- to indirect-gap semiconductor. Raman spectra of MoSe2 monolayers were measured using a range of different excitation energies (Eex = 1.95 eV, 2.54 eV, and 2.71 eV using a Renishaw (Ramascope), and Eex=2.33 eV using Horiba (Jobin Yvon HR800), in each case, the incident laser was focused to a spot size of ~1µm using a 100× objective, with the laser power used ~0.4 mW. Monolayer MoSe2 is a direct band-gap semiconductor.61 Past experiment of ARPES measurements on MBE-grown samples suggested that the band gap of MoSe2 (defined as the energy gap between the conductance band minimum and the valence band maximum, ECBM–EVBM) = 1.58 eV.62 However, simultaneous measurements of STM tunneling spectrum and optical measurements (Photoluminescence measurements)63 suggest that the quasiparticle band gap is much higher, between 2.1 – 2.2 eV, while the optical band gap is around 1.55 eV (corresponding to the excitonic A peak), their difference accounted for by its unusually high excitonic binding energy (~0.5 eV) in 2DMoSe2.64,65 Hence our excitation energy range covers a range of values from below to above the quasiparticle band gap, around the C-exciton 2.5 eV66,67, and beyond. A number of past works have reported the Raman spectrum of monolayer MoSe2 within 100 cm1

– 700 cm-1 range of vibrational frequency (Raman shift) values. A survey of these previous

works reveal rich vibrational spectroscopic information in monolayer MoSe2 when measured in mechanically exfoliated samples.46,47,68 However, reports of Raman spectra in CVD-grown samples (which are conventionally thought to have poorer electronic and optoelectronic properties) usually reveal only the two main peaks, i.e. the out of plane mode A’1 (Γ) peak at


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approximately 240 cm-1, and the in-plane mode E’TO peak approximately at 285 cm-1,52,54,55 with the other resonant or multi-phonon peaks being either too weak to be detected, or are untraceable in the background luminescence arising from disorder and impurities in the sample. [We note that CVD-grown 2D MoSe2 show clear low-wavenumber (sub – 30 cm-1) peak features which were beyond our instrument limit]50. Figure 2a shows the Raman shift spectra for wavenumbers (ω) ranging from 100 cm-1 – 650 cm-1 for all four excitation energies, measured in our VPCgrown samples, which clearly demonstrate a range of vibrational peaks that were previously shown to occur in high-quality mechanically-exfoliated samples.47


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Figure 2. Raman spectra of VPC-grown monolayer MoSe2 at different excitation energies: 1.95 eV, 2.33 eV, 2.54 eV and 2.71 eV. The peaks were normalized with respect to the -1

intensity of the Si Peak at 520 cm . The various peaks were labelled in terms of the nearest vibrational modes obtained in our theory calculations and matched with previous reports (see text). The peak features are observed to appear or grow more prominent as the excitation energy changes. The most noticeable ones are discussed in the main text. (b). Evolution of the peak intensity ratio of the A’ and E’ peaks (at ~240 cm-1 and ~285 cm-1, respectively), which demonstrates a sharp resonance around energies close to the C-exciton of monolayer MoSe2. (c) A similar resonant feature is observed in the excitation-energy dependence of the peak intensity ratio of the 2ZA and E’ peaks (at ~250 cm-1 and ~285 cm-

Since the measured intensity of any peak feature seen here is dependent on a number of parameters, we will refrain from comparing the absolute peak-heights. The data presented have been normalized to the intensity of the silicon ~520 cm-1 peak in order to improve visual clarity.


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In this manner, we are able to compare relative peak-height ratios and spectral positions. We note that even though we use the same incident laser power values, when the silicon peak is normalized, there is an overall increase in the spectral weight at the higher excitation energies, which is consistent with the overall growth of absorption of these samples with increasing photon energies.47 There are several important features noticeable in our Raman spectra. Firstly, at all laser

excitation values, the well-known mode for monolayer MoSe2 are observed around ω=240

cm-1. The second signature peak, E’TO was found to vary between ω=282 cm-1 – 288 cm-1 as the excitation energy was varied, very likely due to a switching from the lower-energy TO mode to the higher energy LO modes near the Γ-point of the Brillouin zone with changing excitation

energy.46,47 Both the and E’ peaks become more prominent with increasing excitation energy

values. This growing spectral prominence with increasing excitation energy can be partially attributed to the growing optical absorbance of MoSe266 as the excitation energy increases from

1.95 eV – 2.71 eV. However, the peak grows significantly more sharply compared to the E’

peak, a feature which has been brought out clearly in figure 2b, which shows the excitationenergy dependence of the intensity ratio of these two peaks. The ratio grows sharply with increasing excitation energy, and then falls dramatically beyond 2.6 eV, thereby demonstrating a resonance-like behavior. Interestingly, the resonance occurs away from the quasiparticle band

gap, which is expected to be between 2.1-2.2 eV in monolayer MoSe2, although it is extremely close to the C-exciton ground state of monolayer MoSe2, which is expected to exist between 2.52.6 eV.66,67 We therefore believe that the A’ peak couples strongly to the C-excitons in monolayer MoSe2. We further observe a broad peak centered around 150 cm-1, which we attribute to the overlapping contribution from the longitudinal acoustic phonon mode LA(M) at


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ω=150 cm-1 and the multiphonon process E’–LA(M), around ω=135 cm-1, as indicated in figure 2a. In addition, at the two higher excitation energies, we clearly detect a peak at ω=170 cm-1, which in the monolayer can be attributed to the E” peak at the Γ-point of the Brillouin zone (figure 3). However, this peak is expected to be absent in the monolayer when using the backscattering geometry in the Raman acquisition, similar to the one we are using, thus the peak could be caused by a resonant process or a some sort of interaction with the substrate (note that only appears for some excitations in figure 2a). On the other hand, this peak can appear in bilayer systems (or even number of layers) as a E2g, or in trilayer system (or odd number of layers, except one) as E’2, and hence can be observed69 (See figure 6b). At higher vibrational frequencies, we observe the LA(M) overtones, i.e. the 2LA(M) peak at ω=303 cm-1, the 3LA(M) peak at ω=451 cm-1, and the 4LA(M) peak at ω=590 cm-1. Finally, the peak at ω=352 cm-1 (" (Γ)), present in few layered systems of MoSe2, shows up in our

monolayer, possibly due to resonance effects. From figure 2a, we find that the peaks ω=170 cm-1

and ω=352 cm-1 are nearly absent or untraceable for the two lower energy values, whereas they are clearly present at the higher excitation energies. The rest of the peaks are labeled as a combination of optical and acoustical phonons from M point, which is consistent with recently published work on exfoliated MoSe2 samples.47 We believe that observation of these higherorder and multi-phonon peaks (which are usually absent in CVD-grown samples) is a testament of the high sample quality obtained despite using a vapor-phase growth process. In addition to these expected Raman peaks, we observe the clear appearance of a peak at ~250 cm-1, whose origin has not been clearly established earlier. Interestingly, although this peak does not appear in Raman spectra of conventional CVD-grown MoSe2, it does show up in CVDgrown alloy-like and heterostructures of MoSe2 with other 2D materials, which has led to some


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conjecture that this peak is possibly related to the formation of MoSe2-MoS2 alloys.57 Moreover, the position of this peak is very close to the inter-layer

E 22g

shear mode at the M point, expected

to appear at ~248 cm-1, but only in multi-layer or bulk samples,46 However, we are able to observe a peak at this position very clearly in pure-phase monolayer MoSe2, as have Soubelet et al. in their mechanically-exfoliated samples, establishing that this peak is intrinsic to monolayer MoSe2. Inspection of the phonon dispersion (shown later) reveals no vibrational bands at this energy at the Γ-point. However, it is very close to twice the energy of the ZA branch near the M point, and with our theoretical evidence, we propose this peak is the double resonance of the ZA, i.e. 2ZA, thus we label it accordingly in Figure 2a. Figure 2c shows the variation of the intensity ratio, I2ZA/IE’, as a function of Eex. As with the A’ and E’ peaks, we find that although both 2ZA and E’ peaks grow with Eex, the ratio of their intensity grows sharply, peaks around Eex ~ 2.5 eV, and then drops sharply again. We therefore believe that the observed ~250 cm-1 peak also couples with the C-excitons in monolayer MoSe2.


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E’

A’1

ZA Figure 3. (a) Real-space schematic of the two principle modes E’ and A’1 along with the proposed ZA mode (b) Phonon dispersion of monolayer MoSe2. The various vibrational bands as labeled. (c) Calculated vibrational density of states (VDOS) for monolayer MoSe2. In order to have a better understanding of the experimental results and in particular for the Raman signal around 250 cm-1, we performed the density functional perturbation theory (DFPT) calculation to obtain the phonon dispersion of a MoSe2 single layer and the density of vibration states, shown in figure 3.Figure 3b-c presents the band structure and density of phonon states in monolayer MoSe2. The phonon dispersion in Figure 3b shows the vibration modes calculated

along the Γ MKΓ high symmetry lines in the first Brillouin zone. As such both the Raman

and Infrared active modes are displayed. The phonon dispersion exhibits an almost flat phonon band around ~125 cm-1 along the M—K line and the crossing of the TA and ZA at two points along the chosen high symmetry path. The description of the possible Raman activities of the

zone-center phonons will be relevant to our discussion since they are consequential to mode

assignments in Figure 2a. By symmetry, the highest lying modes at Γ, namely " Γ , is only


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Infrared (IR) active while Γ is IR and Raman active mode, and the modes " Γ , and Γ

are only Raman active, that is why the peak at 350 cm-1 could come from a higher order resonant

process or due to substrate interaction. Note that this signal is present in bilayer or more layer systems.69 From Figure 3b it can be noted that there are no phonon modes crossing the 250 cm-1 at gamma, meaning that the 250 cm-1 peak is likely to be a second-order Raman mode from a double resonance process involving the acoustic mode (ZA) ωZA(q)~125 cm-1, at the M-point, Kpoint or at several q-points along the M-K line. The possible double scattering involving ω(q)and ω(-q) amounts to doubling the frequency ω(q). The vibrational density of phonon states (figure 3c) around 125 cm-1 confirms the presence of several phonons with frequencies 125 cm-1 that can play a role in the double resonance process. We propose that the double resonance effect is due to electron-phonon interactions and also to exciton-phonon interactions. First, we consider the double resonant Raman processes 2ZA taking into account the electrons and phonons. For this task, we have computed the intensity resulting from the Fermi golden rule generalized to the perturbative fourth order given by76:

, ∝ , ,, 2 2 2

where MAB indicate transition (vertical transition), and electron-phonon coupling matrices; is

the excitation energy; , , are the energies of the excited crystal (electrons and phonons),

and is the energy of the final state of the scattering; , , are the inverse of the lifetime of the electronic excitations A, B and C respectively.

We assume further that the matrices MAB are constant and focus on the denominator of the expression above. Using this assumption, we approximated the double resonance Raman


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intensity for monolayer MoSe2 and focused on the frequency region 250 cm-1 as depicted in Figure 4a for 2 excitation wavelengths, 632 and 488 nm. This figure shows clearly the presence of a double resonance peak with high intensity at ! "250 cm-1 with a 488 nm (2.54 eV) excitation, thus confirming the experimental result (see figures 2a and 2c). One can get a

physical insight regarding this process if we plot the isoenergy contour in the Brillouin zone and the band structure. First, to explain the electronic transition from the valence band to the conduction band close to K, the isoenergy contour at 2.54 eV (488 nm) is calculated (See figure 4b).

Figure 4. (a) Double resonance Raman intensities obtained from the generalized Fermi Golden rule using 2 excitation wavelengths 632 and 488nm. (b) Hexagonal Brillouin zone of MoSe2 showing the isoenergy contour (dotted line) formed at 2.54 eV (488 nm) closed to the K points. T1 and T2 are points in the isoenergy contour connected by the ZA(M) phonon. (c) Electronic band structure of MoSe2 (without spin-orbit coupling for clarity) showing the transition of an electron to the conduction band and scattered by the ZA(M) phonon from T1 to T2 and back (in red). Note that 2.26 eV corresponds to the quasiparticle band gap (d) imaginary part of the dielectric function calculated with BSE showing the A exciton at 1.64 eV, the B exciton at 1.84 eV and the C exciton at 2.34 eV. The red line indicates the 2.54 eV where the experimental C exciton is located.


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Then, once an electron is excited to the point T1 in the conduction band (see figure 4c), the ZA(M) phonon scatters the electron to the point T2 in the isoenergy contour. Now, the same phonon (ZA(M)) scatters back the electron to T1, thus producing the double resonance effect. These theoretical results are consistent with the experimental data obtained from Soubelet et. al.47 when they report by using polarization resolve Raman scattering that the peak at around 250 cm-1 is an out of plane mode.

To shed light on the role of excitons, we have calculated the imaginary part of the dielectric function Im (ε) including excitonic effects by solving the Bethe-Salpeter equation (BSE) including spin orbit coupling79. The energy dependence of Im (ε) exhibits a measure of the photon absorption of the system, thus showing the excitonic transitions in our system. In figure 4d we can see the signal associated to the A and B excitons at 1.64 eV and 1.84 eV respectively, however for the C exciton, which in the literature has been related to the next high intensity peak in the absorption spectrum, in our calculations expresses at around 2.34 eV in accordance to other computations reported in the literature63. Experimentally this peak is around 2.5 eV63,64 and the difference between theory and experiment is due to electron-phonon interactions, not considered in our calculations, which play an important role at high energies63. Above we have shown that when we considered just electrons and phonons, the system will have a double resonance effects due to electron-phonon scattering at 2.54 eV excitation. Returning to our experimental data, it is expected that certain Raman-active phonon bands will have measurable dispersions in the ω–q plane of the band structure, which will show a variation of positions as a function of laser energy. In our case, the phonon modes were found to be quite stiff,

and

small

but


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Figure 5. (a) Magnified Raman spectra of monolayer MoSe2 to showing the evolution of the 2ZA and E’ peaks with different excitation energies. Insets highlight the variation of their positions as a function of excitation energies. (b) Raman spectrum of a sample measure after six months of synthesis, where the 2ZA peak seems to weaken or disappear

systematic variations could be found in some of the modes. Figure 5a shows a magnified version of the Raman spectra between ω = 220 cm-1–320 cm-1, highlighting the excitation-energydependent evolution of the positions of the 2ZA and E’ peaks. The insets of this figure show the evolution of the position 2ZA and E’ peaks as a function of the energy excitation. It can be observed that both the 2ZA and E’ peaks red-shifts to lower frequencies as the excitation energy increases. Very interestingly, the 2ZA peak becomes indiscernibly weak in samples which remain stored for some time. Figure 5b shows the Raman spectrum of a monolayer sample that was stored for six months. The arrow marks the region where the 2ZA-peak should appear, where only a very weak feature is seen, in comparison to that seen in figure 5a, which was taken from the freshly-prepared sample. Since it is well-known that ageing has a distinctly deleterious impact on these 2D materials, one could argue that the 2ZA peak is a very sensitive signature of


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the sample quality. This can well be the reason why often the 2ZA peak is not seen in conventional CVD-grown samples.54 Finally, we present Raman spectroscopic data of our VPC-grown MoSe2 as a function of sample layer-thickness. The determination of layer-thickness is vital in atomically-thin TMDs, as changing the number of layers from one to few, or from odd to even result in remarkable changes in electronic, optical, and spin-dependent properties. For example, as the layer-thickness is increased beyond 1, 2D-MoSe2 becomes an indirect band-gap system with strongly suppressed photoluminescence, as shown in figure 1f. The crystallographic symmetry undergoes a systematic alternation between odd and even layers, as these layers alternate between centrosymmetric (even layers) to non-centrosymmetric (odd-layered) crystals. Recent work has shown that such symmetry-inversions play a strong role in determining the strength of valleyHall effect in 2D transition metal dichalcogenides.12,17 While the layer-thickness dependent studies have been performed extensively for 2D MoS2, a similar investigation on the few-layered 2D-MoSe2 system has been only recently reported, in mechanically exfoliated samples. Here, we present layer-thickness-dependent investigation of Raman spectra in our VPC-grown samples, and show that not only are the intricate Raman features retained in our high-quality samples, but also present previously un-reported approaches for discerning layer-thickness values of atomically-thin MoSe2 samples. Figure 6a shows an optical image of a typical MoSe2 sample where

VPC

growth

leads

to

multi-layered

regions


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Figure 6. Optical image of a typical MoSe2 sample with multiple layers, in which layerthickness dependent Raman (and photoluminescence, fig. 1f) spectra were investigated (scale bar = 10 µm). (b) Typical layer-thickness-dependendent Raman spectra of MoSe2, shown here for an excitation energy of 2.71 eV. The spectra were normalized with respect to the silicon 520 cm-1 peak, and then shifted vertically for clarity. The relative intensity of the A’ and E’ peaks change with layer thickness, as does the position of the E’ peak. (c) Variation of

the intensity ratio between the /A1g and the E’/E12g peaks as a function of layer-thickness, shown for four different excitation energy values. (d) Variation of the E’/E12g peak position as a function of layer thickness, shown for four different excitation energy values.


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within the same sample, with the layer-thickness values are identified as labeled. Raman spectra were measured using all four excitation energies as before on several areas within an identified layer-thickness regions. Figure 6b shows the layer-thickness dependent Raman spectra measured using Eex = 2.71 eV (λex = 457 nm). The overall spectral intensities were found to vary substantially with layer thickness values, and hence, we normalized each spectrum with respect to the peak height of the Si 520 cm-1 peak, and then shifted them vertically to enhance visual

clarity. The well-known and E’ modes for monolayer MoSe2 are observed at 240 cm-1 and 286 cm-1 respectively. (We use Eg and A1g notations for bilayer MoSe2 since single, bilayer (even

numbers) and bulks belong to different point groups D3h, D3d, D6h). We find that there is the

sharp decrease in the /A1g peak intensity and increase in E’/# peak intensity as the layer-

thickness grows. In addition, while the /A1g peak demonstrated no change in position with

increasing number of layers, the E’/# peak position decreases systematically as the numbers of

layers increases. These two variations are clearly brought out in figure 6c-d. Figure 6c presents the variation of the intensity ratio of the peaks A’/A1g and E’/ # with layer-thickness, shown

for different excitation energy values. For both excitations, the peak-intensity-ratio decreases with increasing layer-thickness values. Very interestingly, however, the change is substantially sharper for Ex=2.54 eV which resonates very closely with the C-exciton in MoSe2.66,67 We attribute this to the sharper resonance of the A’ mode with the C-exciton in the monolayer sample compared to those present in the thicker layers. The variation of intensity ratios of signature peaks have often been used in the past for other 2D materials such as graphene77,78 providing a way to correlate the number of layers. However, to the best of our knowledge, such a relationship as shown in figure 6c has never been reported for 2D MoSe2. Figure 6d shows the

variation of E’/# peak position as a function of incident laser excitation. We find a clear red-


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shift of this peak to lower frequencies as the number of layers increases. This is possibly due to the sensitivity of the in-plane vibrational modes to the presence of additional layers, mediated peak position provides an through van der Waals interactions. This decrease in the E’/#

additional method for discerning various layer-thicknesses in atomically-thin MoSe2. And finally, we note that a peak appears close to ~250 cm-1 at certain layer-thicknesses, close to the position of the monolayer 2ZA mode as well as the inter-layer

E 22g shear

mode at the M point in

multi-layered MoSe2.46 Owing to this uncertainty, the layer-thickness-dependence of this peak was not presented.

CONCLUSIONS: We have grown large-area high quality single and few-layered MoSe2 samples by direct selenization of MoO2 powder using a VPC method. Raman spectra of monolayer and few-layer MoSe2 have been investigated using four different excitation energies. We demonstrate experimentally that the A’1 peak as well as an additional peak at ~250 cm-1 in monolayer samples couple strongly to the C-exciton close to the 2.54 eV laser excitation. We have shown that the peaks at 170 cm-1 and 350 cm-1 can be observable at high excitation energies even though it is forbidden in the backscattering geometry. We further show theoretically, for the first time that the peak at 250 cm-1 for monolayer MoSe2 is related to a double resonant process of the acoustic mode (ZA) involving the C-exciton and electron-phonon interactions. We also demonstrate that both the 2ZA and E’ peaks red-shifts to lower frequencies as the excitation energy increases. Additionally, the 2ZA peak becomes absent on aged samples. To utilize Raman spectroscopy as a tool to characterize MoSe2 samples of varying layer-thickness, we have also presented the

intensity ratio between the /A1g and the E’/E12g peaks with four different excitation energy


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values. We believe that these results shine significant light on the Raman modes in 2D-MoSe2, especially a first possible explanation of the 250 cm-1 mode, and the demonstration of excitonsphonon coupling in this material, similar to how they have been recently observed in other 2D systems.80,81The detailed observations possible on our recently-developed VPC-synthesized samples are highly encouraging for both fundamental and applied research in TMDs in general.

METHODS: Experimental. MoSe2 flakes were synthesized using MoO2 (molybdenum dioxide) and selenium powder in a quartz-tube-in-a-furnace vapor-phased deposition system. Samples were grown on Si/SiO2 and quartz substrates which were placed face down on an alumina boat that included dry MoO2 powder at center of the furnace. A second container with selenium powder was placed upstream of the 1-inch quartz tube. Predominantly monolayer samples could be obtained by ramping-up the furnace to 750 °C at a rate of 15 °C/min and maintaining the setup at this temperature for 20 minutes. During growth, the selenium powder was kept between 150 and 300 degrees (with the lower temperature ranges being suitable for monolayer growth) releasing selenium vapor which was carried into the chamber using a continuous flow of Argon (200 sccm) mixed with H2 (around 3 sccm) at ambient atmospheric pressure, which resulted in the sample growth on the substrates. The chamber was then allowed to cool down naturally. During the growth process, samples of various shape/symmetry were obtained depending on the relative concentration of hydrogen gas used. To obtain multilayer MoSe2 samples, the growth temperature was ramped up to 950 °C while maintaining all other conditions identical as those for monolayer growth.


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Computational. The phonon frequencies along the high-symmetry line Γ-M-K-Γ and the vibrational density of states (VDOS) were computed by diagonalizing the Interatomic Force Constant (IFC) matrix generated using a 4×4×1 q-grid in the Brillouin zone. These methods follow the prescription of DFPT.70 The electronic band structure was also obtained by first principles Density functional theory (DFT)71 using the Quantum-espresso package72. Under the Local Density Approximation (LDA)73 of the exchange-correlation functional and normconserving pseudopotentials following the Trouiller-Martins scheme74 to model the interaction between core and valence electrons of Mo and Se atoms. The geometry of MoSe2 was optimized using 9×9×1 Monkhorst-Pack grid75 to sample the Brillouin Zone(BZ) and the equilibrium condition was imposed using a force threshold of 0.0025 eV/Å (10-4 Ry/bohr ~ 10-3Ha/Å). These parameters have shown to yield satisfactory convergence of the total energy. The lattice parameter of the ground state of the monolayer MoSe2 we obtained was a=3.28 Å and the out-ofplane dimension was set at c=24.65 Å. Energy convergence tests have also been carried out regarding c and the vacuum distance of 24.65 Å satisfactorily limit the inter-layer interaction. DFT is known to yield a lower band gap than experimentally observed; hence the electronic band structure was corrected using a rigid shift of the excited states with a scissor operator to the GW quasiparticle band-gap value of 2.26 eV63 To shed light on the role of excitons, we have calculated the imaginary part of the dielectric function ε including excitonic effects by solving the Bethe-Salpeter equation (BSE) including spin orbit coupling using the code YAMBO79. A 72 x 72 gamma centered k-point grid was used for the wavefunctions.79 Conduction bands were used for the calculation of the static dielectric screening which was expanded with a cutoff of 4 Hartree. A cutoff of 4 Hartree was also used for the screened coulomb potential matrix.


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The BSE kernel was constructed using 4 conduction bands and 4 valence bands. A scissor shift of 0.76 eV was used to 2.26 eV to agree with the GW calculations63

ACKNOWLEDGEMENTS: SK acknowledges financial support from the National Science Foundation, NSF ECCS 1351424, and a Northeastern University Tier 1 Provosts Interdisciplinary seed grant. IB acknowledges the support from Republic of Turkey Ministry of National Education. ADM acknowledges the LDRD program at Los Alamos National Laboratory. AR, ML and HT are grateful to the NSF project EFRI-1433311 and to the supercomputing time provided by the CCI at Rensselaer Polytechnic Institute and the XSEDE project TG-DMR17008 which is supported by the NSF grant ACI-1053575.. We thank Dr Sanghyun Hong and Prof. Yung Joon Jung for help with some Raman microscopy measurements.


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REFERENCES

1

Pere Miró,

Martha Audiffreda

and

Thomas Heine. An Atlas of Two-

Dimensional Materials. Chem. Soc. Rev. 2014, 43, 6537-6554.

2

Jimin Kim, Seung Su Baik, Sae Hee Ryu, Yeongsup Sohn, Soohyung Park,

Byeong-Gyu Park, Jonathan Denlinger, Yeonjin Yi,Hyoung Joon Choi, Keun Su Kim. Observation of Tunable Band Gap and Anisotropic Dirac Semimetal State in Black Phosphorus. Science 2015, 349, 723-726.

3

C. Poellmann, P. Steinleitner, U. Leierseder, P. Nagler, G. Plechinger, M. Porer, R.

Bratschitsch, C. Schüller, T. Korn & R. Huber Resonant Internal Quantum Transitions and Femtosecond Radiative Decay of Excitons in Monolayer WSe2. Nat. Mater. 2015, 14, 889-893.

4

Rivera , Seyler KL, Yu H, Schaibley J, Yan J, Mandrus DG, Yao W, Xu X. Valley-

Polarized Exciton Dynamics in a 2D Semiconductor Heterostructure. Science 2016, 351, 688-691.

5

Davide Costanzo, Sanghyun Jo, Helmuth Berger & Alberto F. Morpurgo. Gate-

Induced Superconductivity in Atomically Thin MoS2 Crystals. Nat. Nanotechnol. 2016, 11, 339-344.


27

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

6

Page 28 of 42

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V.

Grigorieva, S. V. Dubonos & A. A. Firsov. Two-Dimensional Gas of Massless Dirac Fermions in Graphene. Nature 2005, 438, 197-200.

7

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I.

V. Grigorieva, A. A. Firsov. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666-669.

8

Yuanbo Zhang, Yan-Wen Tan, Horst L. Stormer & Philip Kim. Experimental

Observation of the Quantum Hall Effect and Berry's Phase in Graphene. Nature 2005, 438, 201-204.

9

Jun Yan, Yuanbo Zhang, Philip Kim, and Aron Pinczuk. Electric Field Effect

Tuning of Electron-Phonon Coupling in Graphene. Phys. Rev. Lett. 2007, 98, 166802.

10

Jianing

Chen,

Michela

Badioli,

Pablo

Alonso-González,

Sukosin

Thongrattanasiri, Florian Huth, Johann Osmond, Marko Spasenović, Alba Centeno, Amaia Pesquera, Philippe Godignon, Amaia Zurutuza Elorza, Nicolas Camara, F. Javier García de Abajo, Rainer Hillenbrand & Frank H. L. Koppens. Optical Nano-Imaging of Gate-Tunable Graphene Plasmons. Nature 2012, 487, 77-81.


28

Page 29 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

11

Naresh K. Emani, Ting-Fung Chung, Xingjie Ni, Alexander V. Kildishev, Yong P.

Chen, and Alexandra Boltasseva. Electrically Tunable Damping of Plasmonic Resonances with Graphene. Nano Lett. 2012, 12, 5202-5206.

12

Jieun Lee, Kin Fai Mak & Jie Shan. Electrical Control of the Valley Hall Effect in

Bilayer MoS2 Transistors. Nat. Nanotechnol. 2016, 11, 421–425.

13

Sanfeng Wu, Jason S. Ross, Gui-Bin Liu, Grant Aivazian, Aaron Jones, Zaiyao Fei,

Wenguang Zhu, Di Xiao, Wang Yao, David Cobden & Xiaodong Xu. Electrical Tuning of Valley Magnetic Moment Through Symmetry Control in Bilayer MoS2. Nature Phys. 2013, 9, 149-153.

14

Timothy C. Berkelbach, Mark S. Hybertsen, and David R. Reichman. Theory of

Neutral and Charged Excitons in Monolayer Transition Metal Dichalcogenides. Phys. Rev. B 2013, 88, 045318.

15

Jingzhi Shang, Xiaonan Shen, Chunxiao Cong, Namphung Peimyoo, Bingchen

Cao, Mustafa Eginligil, and Ting Yu. Observation of Excitonic Fine Structure in a 2D Transition-Metal Dichalcogenide Semiconductor. ACS Nano 2015, 9, 647-655.

16

Xiaofeng Qian, Junwei Liu, Liang Fu, Ju Li1. Quantum Spin Hall Effect in Two-

Dimensional Transition Metal Dichalcogenides. Science 2014, 346, 1344-1347.


29

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

17

Page 30 of 42

Mak KF, McGill KL, Park J, McEuen PL. The Valley Hall Effect in MoS2

Transistors. Science 2014, 344, 1489-1492.

18

L. J. Li, E. C. T. O’Farrell, K. P. Loh, G. Eda, B. Özyilmaz & A. H. Castro Neto.

Controlling Many-Body States by the Electric-Field Effect in a Two-Dimensional Material. Nature 2015, 529, 185–189.

19

Inyeal Lee, Servin Rathi, Dongsuk Lim ,Lijun Li, Jinwoo Park, Yoontae Lee,

Kyung Soo Yi, Krishna P. Dhakal, Jeongyong Kim, Changgu Lee, Gwan-Hyoung Lee, Young Duck Kim, James Hone, Sun Jin Yun, Doo-Hyeb Youn, Gil-Ho Kim. GateTunable Hole and Electron Carrier Transport in Atomically Thin Dual-Channel WSe2/MoS2 Heterostructure for Ambipolar Field-Effect Transistors. Adv. Mater. 2016, 28, 9519-9525.

20

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich , S. V.

Morozov, and A. K. Geim . Two-Dimensional Atomic Crystals. Proc. Natl. Acad. Sci. U.S.A. 2015, 102, 10451-10453.

21

Mas-Ballesté R, Gómez-Navarro C, Gómez-Herrero J, Zamora F. 2D Materials: To

Graphene and Beyond. Nanoscale 2011, 3, 20-30.

22

Y. P. Venkata Subbaiah, K. J. Saji, A. Tiwari. Atomically Thin MoS2: A Versatile

Nongraphene 2D Material. Adv. Funct. Mater. 2016, 26, 2046-2069.


30

Page 31 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

23

Schwierz, F. Graphene Transistors. Nat. Nanotechnol. 2010, 5, 487-496.

24

Ming Liu, Xiaobo Yin, Erick Ulin-Avila, Baisong Geng, Thomas Zentgraf, Long

Ju, Feng Wang & Xiang Zhang. A Graphene-Based Broadband Optical Modulator. Nature 2011, 474, 64-67.

25

Deblina Sarkar, Xuejun Xie, Wei Liu, Wei Cao, Jiahao Kang, Yongji Gong,

Stephan Kraemer, Pulickel M. Ajayan & Kaustav Banerjee. A Subthermionic Tunnel Field-Effect Transistor with an Atomically Thin Channel. Nature 2015, 526, 91-95.

26

Mak, K. F. & Shan, J. Photonics and Optoelectronics of 2D Semiconductor

Transition Metal Dichalcogenides. Nat. Photon 2016, 10, 216-226.

27

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko1, Y.-J.

Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko1, A. K. Geim, C. Casiraghi, A. H. Castro Neto, K. S. Novoselov Strong Light-Matter Interactions in Heterostructures of Atomically Thin Films. Science 2013, 340, 1311-1314.

28

Woo Jong Yu, Yuan Liu, Hailong Zhou, Anxiang Yin, Zheng Li, Yu Huang, and

Xiangfeng. Highly Efficient Gate-Tunable Photocurrent Generation in Vertical Heterostructures of Layered Materials. Nat. Nanotechnol. 2013, 8, 952-958.


31

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

29

Page 32 of 42

Choi MS, Lee GH, Yu YJ, Lee DY, Lee SH, Kim P, Hone J, Yoo WJ. Controlled

Charge

Trapping

by

Molybdenum

Disulphide

and

Graphene

in

Ultrathin

Heterostructured Memory Devices. Nat. Commun. 2013, 4, 1624.

30

Francesco Bonaccorso, Luigi Colombo, Guihua Yu, Meryl Stoller, Valentina

Tozzini, Andrea C. Ferrari, Rodney S. Ruoff, Vittorio Pellegrini. Graphene, Related Two-Dimensional Crystals, and Hybrid Systems for Energy Conversion and Storage. Science 2015, 347, 1246501.

31

Jinhua Hong, Zhixin Hu, Matt Probert, Kun Li, Danhui Lv, Xinan Yang, Lin Gu,

Nannan Mao, Qingliang Feng, Liming Xie, Jin Zhang, Dianzhong Wu, Zhiyong Zhang, Chuanhong Jin, Wei Ji, Xixiang Zhang, Jun Yuan & Ze Zhang. Exploring Atomic Defects in Molybdenum Disulphide Monolayers. Nat. Commun. 2015, 6, 6293.

32

Arend M. van der Zande, Pinshane Y. Huang, Daniel A. Chenet, Timothy C.

Berkelbach, YuMeng You, Gwan-Hyoung Lee, Tony F. Heinz, David R. Reichman, David A. Muller & James C. Hone. Grains and Grain Boundaries in Highly Crystalline Monolayer Molybdenum Disulphide. Nat. Mater. 2013, 12, 554-561.

33

Lin YC, Dumcenco DO, Komsa HP, Niimi Y, Krasheninnikov AV, Huang YS,

Suenaga K. Properties of Individual Dopant Atoms in Single-Layer MoS2: Atomic Structure, Migration, and Enhanced Reactivity. Adv. Mater. 2014, 26, 2857-2861


32

Page 33 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

34

Péter Vancsó, Gábor Zsolt Magda, János Pető, Ji-Young Noh, Yong-Sung Kim,

Chanyong Hwang, László P. Biró & Levente Tapasztó. The Intrinsic Defect Structure of Exfoliated MoS2 Single Layers Revealed by Scanning Tunneling Microscopy. Sci. Rep. 2016, 6, 29726 (2016).

35

Yu Li Huang, Yifeng Chen, Wenjing Zhang, Su Ying Quek, Chang-Hsiao Chen,

Lain-Jong Li, Wei-Ting Hsu, Wen-Hao Chang, Yu Jie Zheng, Wei Chen & Andrew T. S. Wee. Bandgap Tunability at Single-Layer Molybdenum Disulphide Grain Boundaries. Nat. Commun. 2015, 6, 6298.

36

Hao Qiu, Tao Xu, Zilu Wang, Wei Ren, Haiyan Nan, Zhenhua Ni, Qian Chen,

Shijun Yuan, Feng Miao, Fengqi Song, Gen Long, Yi Shi, Litao Sun, Jinlan Wang & Xinran Wang. Hopping Transport Through Defect-Induced Localized States in Molybdenum Disulphide. Nat. Commun. 2013, 4, 2642.

37

Stephen McDonnell, Rafik Addou, Creighton Buie, Robert M. Wallace, and

Christopher L. Hinkle. Defect-Dominated Doping and Contact Resistance in MoS2. ACS Nano 2014, 8, 2880-2888.

38

Ma, N. & Jena, D. Charge Scattering and Mobility in Atomically Thin

Semiconductors. Phys. Rev. X 2014, 4, 011043.


33

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

39

Page 34 of 42

Hennrik Schmidt, Shunfeng Wang, Leiqiang Chu, Minglin Toh, Rajeev Kumar,

Weijie Zhao, A. H. Castro Neto, Jens Martin, Shaffique Adam, Barbaros Özyilmaz, and Goki Eda. Transport Properties of Monolayer MoS2 Grown by Chemical Vapor Deposition. Nano Lett. 2014, 14, 1909-1913.

40

Maria O’Brien, Niall McEvoy, Damien Hanlon, Toby Hallam, Jonathan N.

Coleman & Georg S. Duesberg. Mapping of Low-Frequency Raman Modes in CVDGrown Transition Metal Dichalcogenides: Layer Number, Stacking Orientation and Resonant Effects. Sci. Rep. 2016, 6, 19476 .

41

C. Rice, R. J. Young, R. Zan, U. Bangert, D. Wolverson, T. Georgiou, R. Jalil, and

K. S. Novoselov Raman-Scattering Measurements and First-Principles Calculations of Strain-Induced Phonon Shifts in Monolayer MoS2. Phys. Rev. B 2013, 87, 081307.

42

Andrea C. Ferrari & Denis M. Basko Raman Spectroscopy as a Versatile Tool for

Studying the Properties of Graphene. Nat. Nanotechnol. 2013, 8, 235-246.

43

Gouadec, G. & Colomban, P. Raman Spectroscopy F Nanomaterials: how Spectra

Relate to Disorder, Particle Size and Mechanical Properties. Prog. Cryst. Growth Charact. Mater. 2007, 53, 1-56.


34

Page 35 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

44

Zhong Lin, Bruno R Carvalho, Ethan Kahn, Ruitao Lv, Rahul Rao, Humberto

Terrones, Marcos A Pimenta and Mauricio Terrones Defect Engineering of TwoDimensional Transition Metal Dichalcogenides. 2D Mater. 2016, 3, 022002.

45

Changgu Lee, Hugen Yan, Louis E. Brus, Tony F. Heinz, James Hone and

Sunmin Ryu Anomalous Lattice Vibrations of Single-And Few-Layer Mos2. ACS nano 2010, 4, 2695-2700.

46

Dahyun Nam, Jae-Ung Leec & Hyeonsik Cheong Excitation Energy Dependent

Raman Spectrum of MoSe2. Sci. Rep. 2015, 5, 17113.

47

P. Soubelet, A. E. Bruchhausen, A. Fainstein, K. Nogajewski, and C. Faugeras

Resonance Effects in the Raman Scattering of Monolayer and Few-Layer Mose2. Phys. Rev. B 2016, 93, 155407.

48

Shao-Yu Chen, Changxi Zheng, Michael S. Fuhrer, and Jun Yan. Helicity-

Resolved Raman Scattering of MoS2, MoSe2, WS2, and Wse2 Atomic Layers. Nano Lett. 2015, 15, 2526-2532.

49

G. Kioseoglou, A. T. Hanbicki, M. Currie, A. L. Friedman & B. T. Jonker. Optical

Polarization and Intervalley Scattering in Single Layers of Mos2 and Mose2. Sci. Rep. 2016, 6, 25041.


35

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

50

Page 36 of 42

Maria O'Brien,Niall McEvoy,Damien Hanlon, Kangho Lee, Riley Gatensby,

Jonathan N. Coleman, Georg S. Duesberg Low wavenumber Raman Spectroscopy of Highly Crystalline Mose2 Grown by Chemical Vapor Deposition. Phys. Status Solidi (b) 2015, 252, 2385-2389.

51

Xin Lu, M. Iqbal Bakti Utama, Junhao Lin, Xin Luo,Yanyuan Zhao, Jun Zhang,

Sokrates T. Pantelides, Wu Zhou, Su Ying Quek, Qihua Xiong Rapid and Nondestructive Identification of Polytypism and Stacking Sequences in Few-Layer Molybdenum Diselenide by Raman Spectroscopy. Adv. Mater. 2015, 27, 4502-4508.

52

Jing Xia, Xing Huang, Ling-Zhi Liu, Meng Wang, Lei Wang, Ben Huang, Dan-

Dan Zhu, Jun-Jie Li, Chang-Zhi Gu and Xiang-Min Meng. CVD Synthesis of LargeArea, Highly Crystalline MoSe2 Atomic Layers on Diverse Substrates and Application to Photodetectors. Nanoscale 2014, 6, 8949-8955.

53

Sheng-Han Su, Wei-Ting Hsu, Chang-Lung Hsu, Chang-Hsiao Chen, Ming-Hui

Chiu, Yung-Chang Lin, Wen-Hao Chang, Kazu Suenaga, Jr-Hau He and Lain-Jong Li Controllable

Synthesis

of Band-Gap-Tunable

and Monolayer

Transition-Metal

Dichalcogenide Alloys. Front. Energy Res. 2014, 2, 27.

54

Xingli Wang, Yongji Gong, Gang Shi, Wai Leong Chow, Kunttal Keyshar,

Gonglan Ye, Robert Vajtai, Jun Lou, Zheng Liu, Emilie Ringe, Beng Kang Tay, and


36

Page 37 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

Pulickel M. Ajayan. Chemical Vapor Deposition Growth of Crystalline Monolayer MoSe2. ACS Nano 2014, 8, 5125-5131.

55

Jonathan C. Shaw, Hailong Zhou, Yu Chen, Nathan O. Weiss, Yuan Liu, Yu

Huang, Xiangfeng Duan Chemical Vapor Deposition Growth of Monolayer MoSe2 Nanosheets. Nano Res. 2014, 7, 511-517.

56

Sachin R Suryawanshi, Amit S Pawbake, Mahendra S Pawar, Sandesh R Jadkar,

Mahendra A More and Dattatray J Late. Enhanced Field Emission Behavior of Layered MoSe2. Mater. Res. Express 2016, 3, 035003.

57

Xidong Duan, Chen Wang, Jonathan C. Shaw, Rui Cheng, Yu Chen, Honglai Li,

Xueping Wu, Ying Tang, Qinling Zhang, Anlian Pan, Jianhui Jiang, Ruqing Yu, Yu Huang & Xiangfeng Duan Lateral Epitaxial Growth of Two-Dimensional Layered Semiconductor Heterojunctions. Nat. Nanotechnol. 2014, 9, 1024-1030.

58

Ismail Bilgin, Fangze Liu, Anthony Vargas, Andrew Winchester, Michael K. L.

Man, Moneesh Upmanyu, Keshav M. Dani, Gautam Gupta, Saikat Talapatra, Aditya D. Mohite, and Swastik Kar. Chemical Vapor Deposition Synthesized Atomically Thin Molybdenum Disulfide with Optoelectronic-Grade Crystalline Quality. ACS Nano 2015,9, 8822-8832.


37

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

59

Page 38 of 42

Ayse Berkdemir, Humberto R. Gutiérrez, Andrés R. Botello-Méndez, Néstor

Perea-López, Ana Laura Elías, Chen-Ing Chia, Bei Wang, Vincent H. Crespi, Florentino López-Urías, Jean-Christophe Charlier, Humberto Terrones, and Mauricio Terrones. Identification of Individual and Few Layers of WS2 using Raman Spectroscopy. Sci. Rep. 2013,3.

60

Jianyi Chen, Bo Liu, Yanpeng Liu, Wei Tang, Chang Tai Nai, Linjun Li, Jian

Zheng, Libo Gao, Yi Zheng, Hyun Suk Shin, Hu Young Jeong, Kian Ping Loh. Chemical Vapor Deposition of Large-Sized Hexagonal WSe2 Crystals on Dielectric Substrates. Adv. Mater. 2015,27, 6722-6727.

61

Sefaattin Tongay, Jian Zhou, Can Ataca, Kelvin Lo, Tyler S. Matthews, Jingbo Li,

Jeffrey C. Grossman, and Junqiao Wu. Thermally Driven Crossover From Indirect Toward Direct Bandgap in 2D Semiconductors: MoSe2 versus MoS2. Nano Lett. 2012,12, 5576-5580.

62

Yi Zhang, Tay-Rong Chang, Bo Zhou, Yong-Tao Cui, Hao Yan, Zhongkai Liu,

Felix Schmitt, James Lee, Rob Moore, Yulin Chen, Hsin Lin, Horng-Tay Jeng, SungKwan Mo, Zahid Hussain, Arun Bansil & Zhi-Xun Shen. Direct Observation of The Transition from Indirect to Direct Bandgap in Atomically Thin Epitaxial MoSe2. Nat. Nanotechnol. 2014,9, 111-115.


38

Page 39 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

63

Miguel M. Ugeda, Aaron J. Bradley, Su-Fei Shi, Felipe H. da Jornada, Yi Zhang,

Diana Y. Qiu, Wei Ruan, Sung-Kwan Mo, Zahid Hussain, Zhi-Xun Shen, Feng Wang, Steven G. Louie & Michael F. Crommie. Giant Bandgap Renormalization and Excitonic Effects an a Monolayer Transition Metal Dichalcogenide Semiconductor. Nat. Mater. 2014,13, 1091-1095.

64

Yuan Wang, Shuai Zhang, Di Huang, Jingxin Cheng, Yingguo Li and Shiwei Wu.

Screening Effect of Graphite and Bilayer Graphene on Excitons in MoSe2 Monolayer. 2D Mater. 2016,4, 015021.

65

Chendong Zhang, Yuxuan Chen, Amber Johnson, Ming-Yang Li, Lain-Jong Li,

Patrick C. Mende, Randall M. Feenstra, and Chih-Kang Shih. Probing Critical Point Energies of Transition Metal Dichalcogenides: Surprising Indirect Gap of Single Layer WSe2. Nano Lett. 2015,15, 6494-6500.

66

Daichi Kozawa, Rajeev Kumar, Alexandra Carvalho, Kiran Kumar Amara, Weijie

Zhao, Shunfeng Wang, Minglin Toh, Ricardo M. Ribeiro, A. H. Castro Neto, Kazunari Matsuda & Goki Eda. Photocarrier Relaxation Pathway in Two-Dimensional Semiconducting Transition Metal Dichalcogenides. Nat. Commun. 2014,5, 4543.

67

Yilei Li, Alexey Chernikov, Xian Zhang, Albert Rigosi, Heather M. Hill, Arend

M. van der Zande, Daniel A. Chenet, En-Min Shih, James Hone, and Tony F. Heinz.


39

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 42

Measurement of The Optical Dielectric Function of Monolayer Transition-Metal Dichalcogenides: MoS2, MoSe2, WS2, and WSe2. Phys. Rev. B. 2014,90, 205422.

68

Philipp Tonndorf, Robert Schmidt, Philipp Böttger, Xiao Zhang, Janna Börner,

Andreas Liebig, Manfred Albrecht, Christian Kloc, Ovidiu Gordan, Dietrich R. T. Zahn, Steffen Michaelis de Vasconcellos, and Rudolf Bratschitsch. Photoluminescence Emission and Raman Response of Monolayer MoS2, MoSe2, and WSe2. Opt. Express. 2013,21, 4908-4916.

69

H. Terrones, E. Del Corro, S. Feng, J. M. Poumirol, D. Rhodes, D. Smirnov, N. R.

Pradhan, Z. Lin, M. A. T. Nguyen, A. L. Elías, T. E. Mallouk, L. Balicas, M. A. Pimenta & M. Terrones. New First Order Raman-Active Modes in Few Layered Transition Metal Dichalcogenides. Sci. Rep. 2014,4, 4215.

70

Stefano Baroni, Stefano de Gironcoli, and Andrea Dal Corso. Phonons and

Related Crystal Properties from Density-Functional Perturbation Theory. Rev. Mod. Phys. 2001,73, 515-562.

71

Hohenberg, P. & Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. 1964,136,

B864-B871.

72

Paolo Giannozzi1, Stefano Baroni1, Nicola Bonini, Matteo Calandra, Roberto Car,

Carlo Cavazzoni, Davide Ceresoli, Guido L Chiarotti, Matteo Cococcioni, Ismaila Dabo,


40

Page 41 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

Andrea Dal Corso, Stefano de Gironcoli, Stefano Fabris, Guido Fratesi, Ralph Gebauer, Uwe Gerstmann, Christos Gougoussis, Anton Kokalj, Michele Lazzeri, Layla MartinSamos, et al. QUANTUM ESPRESSO: A Modular and Open-Source Software Project for Quantum Simulations of Materials. J. Phys.: Condens. Matter. 2009, 21, 395502.

73

Kohn, W. & Sham, L. J. Self-Consistent Equations Including Exchange and

Correlation Effects. Phys. Rev. 1965, 140, A1133-A1138.

74

Troullier, N. & Martins, J. L. Efficient Pseudopotentials for Plane-Wave

Calculations. Phys. Rev. B 1991, 43, 1993-2006.

75

Monkhorst, H. J. & Pack, J. D. Special Points for Brillouin-Zone Integrations.

Phys. Rev. B, 1976, 13, 5188-5192.

76

Pedro Venezuela, Michele Lazzeri, and Francesco Mauri. Theory of Double-

Resonant Raman Spectra in Graphene: Intensity and Line Shape of Defect-Induced and Two-Phonon Bands. Phys. Rev. B 2011,84, 035433.

77

Mildred S. Dresselhaus, Ado Jorio, Mario Hofmann, Gene Dresselhaus and

Riichiro Saito. Perspectives on Carbon Nanotubes and Graphene Raman Spectroscopy. Nano Lett. 2010, 10, 751-758.

78

L.M. Malard, M.A. Pimenta, G. Dresselhaus, M.S. Dresselhaus. Raman

Spectroscopy in Graphene. Phys. Rep. 2009, 473, 51-87,.


41

ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

79

Page 42 of 42

Andrea Marini, Conor Hogan, Myrta Grüning, Daniele Varsano. Yambo: an ab

Initio Tool for Excited State Calculations. Comp Phys. Comm. 2009, 180,1392.

80

Bruno R. Carvalho, Leandro M. Malard, Juliana M. Alves, Cristiano Fantini, and

Marcos A. Pimenta Symmetry-Dependent Exciton-Phonon Coupling in 2D and Bulk MoS2 Observed by Resonance Raman Scattering. Phys. Rev. Lett. 2016 114, 136403

81

E. del Corro, A. Botello-Méndez, Y. Gillet, A. L. Elias, H. Terrones, S. Feng, C.

Fantini, Daniel Rhodes, N. Pradhan, L. Balicas, X. Gonze, J.-C. Charlier, M. Terrones, and M. A. Pimenta. Atypical Exciton–Phonon Interactions in WS2 and WSe2 Monolayers Revealed by Resonance Raman Spectroscopy. Nano Lett., 2016 16, 2363–2368


42

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