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Tae Young Jeong, Hakseong Kim, Sang-Jun Choi, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Ki Ju Yee, Yong-Sung Kim, Suyong Jung

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[Spectroscopic studies of atomic defects and bandgap renormalization in semiconducting monolayer transition metal dichalcogenides](https://mdr.nims.go.jp/datasets/11fb6d62-06c9-4ec0-8dcb-37d520c22a6c)

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Spectroscopic studies of atomic defects and bandgap renormalization in semiconducting monolayer transition metal dichalcogenidesARTICLESpectroscopic studies of atomic defects andbandgap renormalization in semiconductingmonolayer transition metal dichalcogenidesTae Young Jeong1,2,5, Hakseong Kim1,5, Sang-Jun Choi3, Kenji Watanabe 4, Takashi Taniguchi4, Ki Ju Yee2,Yong-Sung Kim 1 & Suyong Jung 1Assessing atomic defect states and their ramifications on the electronic properties of two-dimensional van der Waals semiconducting transition metal dichalcogenides (SC-TMDs) isthe primary task to expedite multi-disciplinary efforts in the promotion of next-generationelectrical and optical device applications utilizing these low-dimensional materials. Here, withelectron tunneling and optical spectroscopy measurements with density functional theory, wespectroscopically locate the mid-gap states from chalcogen-atom vacancies in four repre-sentative monolayer SC-TMDs—WS2, MoS2, WSe2, and MoSe2—, and carefully analyze thesimilarities and dissimilarities of the atomic defects in four distinctive materials regarding thephysical origins of the missing chalcogen atoms and the implications to SC-mTMD proper-ties. In addition, we address both quasiparticle and optical energy gaps of the SC-mTMDfilms and find out many-body interactions significantly enlarge the quasiparticle energy gapsand excitonic binding energies, when the semiconducting monolayers are encapsulated bynon-interacting hexagonal boron nitride layers.https://doi.org/10.1038/s41467-019-11751-3 OPEN1 Quantum Technology Institute, Korea Research Institute of Standards and Science, Daejeon 34113, Korea. 2 Department of Physics, Chungnam NationalUniversity, Daejeon 34134, Korea. 3 Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34126, Korea. 4 AdvancedMaterials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 5These authors contributed equally: Tae Young Jeong,Hakseong Kim. Correspondence and requests for materials should be addressed to Y.-S.K. (email: yongsung.kim@kriss.re.kr)or to S.J. (email: syjung@kriss.re.kr)NATURE COMMUNICATIONS |         (2019) 10:3825 | https://doi.org/10.1038/s41467-019-11751-3 | www.nature.com/naturecommunications 11234567890():,;http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-6057-2997http://orcid.org/0000-0002-6057-2997http://orcid.org/0000-0002-6057-2997http://orcid.org/0000-0002-6057-2997http://orcid.org/0000-0002-6057-2997http://orcid.org/0000-0003-3885-9999http://orcid.org/0000-0003-3885-9999http://orcid.org/0000-0003-3885-9999http://orcid.org/0000-0003-3885-9999http://orcid.org/0000-0003-3885-9999mailto:yongsung.kim@kriss.re.krmailto:syjung@kriss.re.krwww.nature.com/naturecommunicationswww.nature.com/naturecommunicationsAtomic defect states in two-dimensional semiconductingtransition metal dichalcogenides (SC-TMDs) are creditedto many intriguing scientific and engineering aspects,such as single quantum emitters1–4, single-atom magnetism5, anddefect-modulating dopings6,7, to name a few. Defect states havethe implications to decide the specific type of SC-TMD, whiledefect-related trap states adjust the position of the Fermi level(EF) with respect to conduction and valence bands6–9. The pre-sence of atomic defects along with charged impurities is alsoknown to limit charged carrier mobilities and induce a strongFermi-level pinning at the metal/SC-TMD interfaces, therebylimiting SC-TMD-based electronic applications10. Thus, exam-ining the origins and spectral locations of defect-induced states isprerequisite to the full utilization of such states in SC-TMDs andthe building-up of TMD-based device functionalities. Experi-mental analyses of such defects typically rely on imaging meth-ods, like transmission electron microscopy (TEM) and scanningtunneling microscope (STM), visualizing the various forms ofatomic defects in SC-TMDs6,7,10–13. Although some STM studieshave provided experimental signatures of the mid-gap states fromatomic defects in SC-TMDs14, the majority of outstandingquestions, such as those concerning the defect-induced mid-gapstates and their spectral locations inside the energy gaps, havemostly relied on theoretical predictions8.We note that spectroscopic investigations of defect-inducedmid-gap states should be accompanied by the identification ofother key SC-mTMD material parameters; the quasiparticleenergy gaps (Eg) and the position of EF inside the gaps. Forexample, chalcogen-atom vacancies (VS, VSe), the most commondefects in S-based and Se-based SC-TMDs, are expected to inducemid-gap states: singlet a1 states forming close to the valence bandand doublet e states forming deep inside the energy gap6,8. Quitesurprisingly, however, experiment and theory have yet to agree onthe most fundamental SC-mTMD property, the quasiparticleenergy gaps. For example, such energy gaps inferred from dif-ferent experiments have varied up to ≈1 eV15, and theoreticallyexpected energy gap sizes also differ depending on the extent ofCoulombic interactions15,16. Accordingly, excitonic-bindingenergies (EB), or the energy difference between quasiparticleand optical energy gaps (Eopt), are reported to vary from a fewhundredth of meV to ≈1 eV17–21.In this article, we carry out careful electron tunneling, opticalspectroscopy measurements, and density functional theory (DFT)calculations for four representative SC-mTMDs—mWS2, mMoS2,mWSe2, and mMoSe2—to accurately assess material parameters,such as the mid-gap states from chalcogen-atom vacancies, thequasiparticle energy gaps and exciton-binding energies, and othermaterial specifications. We are able to identify the mid-gap statesfrom chalcogen-atom vacancies in the SC-mTMDs by introducingh-BN as a tunnel barrier and graphene as a spectrum analyzer invan der Waals (vdW)-based planar heterostructures. Defect-induced mid-gap states in the four respective films reveal simila-rities and dissimilarities regarding the spectral locations of thedefect states, mechanisms of vacancy formation, and overall defectdensity of states (DOS). Our studies suggest that single-atomdefects in SC-mTMDs present direct experimental implicationsthat chalcogen-atom vacancies turn into active charged dopants.Moreover, we can accurately determine the quasiparticle energygaps and exciton-binding energies of the four SC-mTMDs viaelectron tunneling, optical reflectance/transmission spectroscopy,and temperature-dependent photoluminescence (PL) measure-ments. We confirm that the electronic structures of theSC-mTMDs are greatly renormalized by electron–electron inter-actions. With temperature-dependent PL, we then assess theexcitonic-binding energies of these monolayers to be as large as≥ 0.78 eV, when the films are encapsulated by h-BN and graphene.Results2D vdW planar tunnel junctions with SC-mTMDs. An opticalviewgraph and schematic of the vdW heterostructure for probingthe electronic and optical properties of SC-mTMDs are displayedin Fig. 1a. Here, we list a few experimental highlights forimplementing graphene as the bottom contact to a given SC-mTMD. First, direct metal contact to a SC-mTMD induceselectronic and physical deformations on the film, which renderscontact resistances comparable with or even larger than tunnelresistances through the h-BN barriers at low temperatures. Thisadditional resistance along the path of tunnel electrons violatesthe ultimate priori for electronic tunneling spectroscopies,requiring that a major voltage drop occur at the tunnel junctionin order for sample-bias voltage (Vb) to be associated with tunnel-electron energy with respect to the Fermi level (EF). Thus, areliable and low-resistance metal–SC-mTMD contact, which wehave achieved via the bottom graphene, is critical for accuratelyaddressing the electronic structures of SC-mTMDs.The second advantageous role of the graphene bottom contactis that it allows the single-atom carbon layer to be used as aspectrum analyzer. As schematically illustrated in Fig. 1b, tunnelelectrons injected from the graphite probe detect the electronicband structure of the SC-mTMD only if the tunnel electronspossess higher (lower) energies than the conduction (valence)band of the SC-mTMD. Otherwise, tunnel electrons exclusivelydetect the bottom graphene through the energy gap windows ofboth h-BN and SC-mTMD. Thus, any deviations in the spectrafrom the graphite–insulators–graphene tunnel junction, notedhereafter as the graphene baseline, should be attributed to theelectronic structure of the SC-mTMD and the probable mid-gapstates. The third role of the graphene is to minimize probe-induced charging effects. During tunneling measurements, theeffective electric field between the probe and SC-mTMDs throughthe h-BN barrier becomes strong when Vb increases up to |Vb| ≥1 V. Thus, probe-induced charges and consequent electronicstructure modifications in the SC-mTMD could cause seriouscomplications in accurately analyzing tunnel spectra22,23. Thanksto a much larger charge compressibility of the graphene, however,induced charges accumulate only on the bottom graphene whenVb is within the energy gaps, thereby allowing us to probe theintrinsic band structure of the SC-mTMD.Electron tunneling and optical spectroscopy measurements.Figure 1d shows a collection of tunneling spectra, differentialconductance (G= dI/dVb) curves as a function of Vb from mWS2,mMoS2, mWSe2, and mMoSe2 planar junctions at T ≤ 4 K. In ourscheme, Vb is applied to a graphite probe with the SC-mTMD–graphene connected to a current preamplifier. Thus,negative (positive) Vb corresponds to the empty (filled) states ofthe SC-mTMD at a positive (negative) energy with respect to EF.The colored arrows in Fig. 1d, respectively, represent the locationsof the quasiparticle energy gaps of the SC-mTMDs; detailedmethods for locating the energy gaps will be described inlater sections. The inset in Fig. 1d displays a graphene baselinedI/dVb with the Dirac point of graphene tuned at Vb= 0 V, andgreen lines indicate numerical fittings to experimental data (redcircles)22,24. We compare several graphite–h-BN–graphenejunctions and find out that all tunnel spectra maintain similardI/dVb characteristics only differentiated by multiplication con-stants, predetermined by the tunnel h-BN thicknesses and junc-tion areas (Supplementary Fig. 1).Our planar heterojunctions allow us to address both electronicand optical SC-mTMD properties without switching deviceplatforms. Figure 1e shows a collection of PL measurements atT= 300 K and T= 80 K from identical SC-mTMD-based planarARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-11751-32 NATURE COMMUNICATIONS |         (2019) 10:3825 | https://doi.org/10.1038/s41467-019-11751-3 | www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsdevices. The dominant PL peak, identified as an A exciton thatdetermines the optical energy gap of the particular SC-mTMD, ismeasured right at the tunnel junction where the monolayers areencapsulated by thin h-BN and graphite probe on top, andgraphene and thick h-BN on the bottom (Supplementary Fig. 2).As previously reported25,26 and confirmed from our devices, A-exciton peaks of SC-mTMDs blue-shift as temperature decreasesin the range of 80 K ≤ T ≤ 300 K. Following the Varshnirelation25, we extrapolate the A-exciton peak at T= 0 K andassign it as the Eopt of the SC-mTMD encapsulated with grapheneand h-BN, such as Eopt (mWS2)= 2.051 eV, Eopt (mMoS2)=1.936 eV, Eopt (mWSe2)= 1.724 eV, and Eopt (mMoSe2)= 1.638 eV(Supplementary Figs. 3, 4).We can independently measure the spin–orbit coupling (SOC)-induced valence-band splittings by locating the A and B excitonicpeaks through optical reflectance and transmittance measure-ments (Supplementary Fig. 5). The inset in Fig. 1e showsreflectance spectra from the mWS2 device at T= 80 K and T=300 K. Both excitonic peaks are clearly identifiable, as well as A–Bexciton spacing; therefore, the SOC-induced valence-bandsplitting (ΔSO) is determined to be ΔSO (mWS2) ≈ 0.38 eV. Notethat ΔSO is weakly dependent on temperature unlike theindividual peak positions of A and B excitons, and ΔSO is lesssusceptible to the dielectric environments. We prepare severalSC-mTMDs on different substrates and find that the A–B excitonspacings are consistent, within an uncertainty level of ±0.01 eV,with varying dielectric environments and temperatures (Supple-mentary Table 1). With optical measurements, therefore, we candetermine the SOC-induced valence-band splittings of all fourSC-mTMDs: ΔSO (mWS2)= 0.38 eV, ΔSO (mMoS2)= 0.15 eV,ΔSO (mWSe2)= 0.43 eV, and ΔSO (mMoSe2)= 0.20 eV (Supple-mentary Fig. 6).Assessing atomic defects of S-based SC-mTMDs. Figure 2a andc displays tunneling spectra from mWS2 and mMoS2 devices,replotting dI/dVb (Fig. 1d) in log scale. As displayed in Fig. 2a,4.0 3.0 2.0 1.0 0.0 –1.0 –2.0 –3.005101520253035dI/dVb (μS)dI/dVb (S)Vb (V)1.9 2.1 2.3 2.51.021.041.061.08600 650 700 750 800 850 9000.00.20.40.60.81.0Normalized PL intensityWavelength (nm)dWS2MoS2WSe2MoSe2WS2MoS2WSe2MoSe2Energy (eV)ReflectanceWS2eABGraphene/h-BN/graphite–3 –2 –1 0 1 2 310–410–610–810–10Vb (V)SiSiO2h -BNGrapheneMonolayer TMD Tunnel h-BNGraphiteTi/AuIVb532 nm (CW)Ti/Au–-GraphiteTunnel h-BNGrapheneMonolayer TMDEnergyDistance--a b cΔSOΔΓ-KΔQ-KEcEvEF EgEoptEBa1eQ K M ΓΓEnergy20 μmGrapheneMonolayer TMDTunnel h-BNGraphiteEopt (WS2)T < 4.0 KΔSO (WS2) = 0.38 eV0.39 eVT = 80 KT = 300 KTEopt (MoSe2) @80 K300 KEg(MoSe2)Eg(WSe2)Eg(MoS2)Eg(WS2)EF80 K300 KFig. 1 Electron tunneling and optical spectroscopy studies with SC-mTMD vdW heterostructures. a Schematic and optical viewgraph of our mTMD-basedvdW planar heterostructure for electron tunneling and optical spectroscopy measurements. For electron tunneling studies, sample-bias voltage (Vb) isapplied to the top graphite, and tunneling current through the h-BN and SC-mTMD is monitored at the bottom graphene. For optical spectroscopymeasurements, a laser with either continuous 532 nm for PL or supercontinuum white sources for reflectance measurements is incident vertically on themTMD planar tunnel device, and optical signals are collected with a × 50 objective lens. b Simplified energy-band alignments of our SC-mTMD-basedplanar tunnel junctions. Electrons injected from the graphite probe detect either the SC-mTMD or the bottom graphene layer depending on Vb and itsrelative position with respect to the mTMD electronic structures. c Representative energy-momentum dispersion relations for SC-mTMD films depictedwith key material parameters: atomic defect states (a1, e), quasiparticle (Eg) and optical (Eopt) energy gaps, exciton-binding energy (EB), and others.d Series of differential conductance (G= dI/dVb) curves as a function of Vb from mWS2 (blue), mMoS2 (red), mWSe2 (green), and mMoSe2 (orange)planar tunnel junctions at T≤ 4 K. Arrows, respectively, represent the locations of the quasiparticle energy gaps. Inset: a representative dI/dVb spectrumfrom one of the planar graphite–h-BN–graphene tunnel junctions. Green lines indicate numerical fittings to the experimental data (red circles). e Collectionof PL spectra from the SC-mTMD planar devices at T= 300 K (dotted lines) and T= 80 K (solid lines). Inset: reflectance spectra measured at T= 300 K(dotted lines) and T= 80 K (solid lines) from the mWS2 planar tunnel deviceNATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-11751-3 ARTICLENATURE COMMUNICATIONS |         (2019) 10:3825 | https://doi.org/10.1038/s41467-019-11751-3 | www.nature.com/naturecommunications 3www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsspectral features at higher Vb are better identified with normalizedconductance (dI/dVb)/(I/Vb) plots. To better distinguish dI/dVbat lower Vb, we numerically average out the original data and plotthe leveled signals (red lines). Note that signals where Vb is insidethe mWS2 energy gap (|Vb| ≤ 1 V) reveal distinct dI/dVb varia-tions with more than three orders of magnitude, and these spectrareflect the graphene baseline with both h-BN and SC-mTMD astunnel insulators. Interestingly enough, the graphene baseline andthe mWS2 tunnel signals become well aligned in a Vb range of|Vb| < 0.7 V for both filled (Vb > 0 V) and empty (Vb < 0 V) states.After a slight dI/dVb hike at Vb ≈ 0.7 V, the mWS2 spectra followthe graphite–graphene junction characteristics up to Vb < 1.5 Vwith a minor adjustment at the tunneling constant (dotted greenline).As discussed previously, any deviations from the graphenebaseline can be directly related to the SC-mTMD film and itselectronic structure. At first, we assign the dI/dVb peaks at –2.33 eVand –2.21 eV to the valence-band edges of the K and Γ points ofthe mWS2, respectively. In mWS2, the valence-band edge at Γ isexpected to be higher in energy than the lower edge of the SOC-split valence band at K. Directly inferred from the opticallydetermined ΔSO (mWS2)= 0.38 eV, the higher SOC-split valenceband, thus the valence-band edge of mWS2, should be positionedat –1.95 eV, where we locate a distinct dI/dVb tunnel feature(Supplementary Fig. 7). Following the same approach, theconduction-band edge at K is assigned at 0.93 eV, and the dI/dVb peak at 1.05 eV as the conduction-band edge at the Q point.Accounting for all these assignments, the mWS2 film encapsu-lated with nonperturbing high-quality h-BN and graphene isconfirmed to be a direct bandgap n-type semiconductor, whoseconduction band is closer to EF than the valence band edge, andwith a quasiparticle energy gap Eg= 2.88 eV, excitonic-bindingenergy EB= 0.83 eV, and an optical energy gap Eopt= 2.051 eV.The uncertainty for each energy-level assignment is less than± 0.01 eV. Complete energy-level alignments for mWS2 aresummarized in the diagram in Fig. 2b. We point out that themeasured quasiparticle energy gap of mWS2 is in perfectagreement with theoretical expectations from the GW approachconsidering many-body perturbation effects.We now address the mMoS2 electronic band structuresfollowing the above-discussed spectra-analyzing protocol withgraphene baseline. As displayed in Fig. 2c, the graphene baselinefollows most of the dI/dVb features from the mMoS2 device in thefilled states at Vb < 1.5 V. It is intriguing to note that, identical tomWS2, a slight dI/dVb increase in value is also present at Vb ≈0.7 V in mMoS2. Our measurements indicate that the valence band48121620242.5 2.0 1.5 1.0 0.5 0.0 –0.5 –1.0 –1.510–410–510–610–710–810–910–1010–410–510–610–710–810–910–10dI/dVb (S)Normalized dI/dVbNormalized dI/dVbdI/dVb (S)Vb (V)2.5 2.0 1.5 1.0 0.5 0.0 –0.5 –1.0 –1.5Vb (V)10203040a bGraphite/h-BN/grapheneΔSOΔΓ-KΔΓ-K, ΔSOΔQ-KΔQ-KEg = 2.88 eVEg = 2.72 eVmWS2mMoS2EFEFc dKQΔQ-K = 0.12 eVΔQ-K = 0.15 eVEB = 0.83 eVEB = 0.78 eVEg = 2.88 eVEg = 2.72 eVEopt = 2.051 eVEopt = 1.936 eVΔSO = 0.38 eVΔΓ-K = 0.26 eVΔSO = 0.15 eVΔΓ-K = 0.15 eVEv = 1.95 eVEv = 1.86 eVEc = 0.93 eVEc = 0.86 eVCBMVBMEFEFmWS2mMoS2KΓKQCBMVBMKΓ(± 0.01 eV)1.21 eV1.30 eV–1.95 eVeV–2.33 eeV–2.21 eV1.05 eV–2.01 eV–1.86 eV0.86 eV1.01 eV0.93 eV1.17 eV1.17Fig. 2 Detailed electronic structure analyses from electron tunneling spectroscopy measurements of S-based mTMDs. a, c Tunnel spectra plotted withdI/dVb in log scale from the mWS2 (a) and mMoS2 (c) planar tunnel junctions. Solid and dotted green lines mark the graphene baselines. Normalizedconductance (dI/dVb)/(I/Vb) plots (blue solid lines) better represent tunneling spectra features at higher Vb. The areas delineated with purple and orange,respectively, represent the a1 and e defect states from sulfur-atom vacancies. dI/dVb spectral locations and key electronic structure assignments for themWS2 (a) and mMoS2 (c) films are marked with dotted black lines and solid red arrows. b, d Summarized energy-level assignments for the mWS2 (b) andmMoS2 (d) films. Uncertainty for each energy-level assignment is less than ±0.01 eVARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-11751-34 NATURE COMMUNICATIONS |         (2019) 10:3825 | https://doi.org/10.1038/s41467-019-11751-3 | www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsedge at Γ is in alignment with the lower SOC-split band edge at theK point at –2.01 eV, and the dI/dVb feature at –1.86 eV where thetunnel spectra in log scale evidently changes its slope is assigned asthe higher SOC-split valence-band edge at K (SupplementaryFig. 7). The valence-band splitting at K is in perfect agreementwith optically confirmed ΔSO (mMoS2)= 0.15 eV.Analyzing the mMoS2 dI/dVb in the empty states, however, is notas straightforward as for mWS2 or the filled states of mMoS2. Atfirst, dI/dVb in the empty states are significantly larger than thevalues in the filled states, by more than two orders of magnitude,making mMoS2 dI/dVb highly asymmetric around EF. Interestinglythough, dI/dVb becomes realigned with the graphene baseline atVb ≈ –0.8 V with a significantly enhanced dI/dVb multiplicationconstant. With that, we assign the conduction band edge of themMoS2 at the K point at 0.86 eV, and the dI/dVb peak at 1.01 eV asthe band edge at Q. As a result, mMoS2 can be considered as adirect bandgap n-type semiconductor, with a quasiparticle energygap Eg= 2.72 eV and excitonic-binding energy EB= 0.78 eV(Eopt= 1.936 eV). Again, the experimentally assessed quasiparticleenergy gap of the mMoS2 is in excellent agreement with thepredicted energy gaps from GW calculations15,27.We relate the enormously amplified dI/dVb in the empty statesto the doublet e defect states from sulfur-atom vacancies in themMoS2. Based on our DFT calculations, the majority of singlet a1states in mWS2 are formed at lower energies than the valence-band edge, concealing most of the defect states under the valenceband (see below). The bulk portion of a1 states in mMoS2,however, are expected to form at higher energies than the valence-band edge, expecting rather pronounced a1-related mid-gap states.Defect states relating to the doublet e states are formed deep insidethe energy gaps with the mid-gap states in mMoS2 closer to EF inthe empty states. Our measurements confirm these theoreticallyexpected spectral locations of a1 and e defect states in S-based SC-mTMDs. We specify that the dI/dVb regions, positioned higher inenergy than the valence-band edges, therefore within the energygaps with dI/dVb straying from the graphene baseline (depicted inpurple in Fig. 2a, c), reflect the a1 defect states. It is obvious thatthe a1 states in mMoS2 extend further into the gap whencompared with the smaller dI/dVb region for the mid-gap states inmWS2. In addition, an evident dI/dVb hump inside the energy gapof mWS2, as marked with a red arrow and delineated in orange inFig. 2a, is assigned to the e defect states, and their spectrallocations are consistent with theoretical calculations (see below).We further note that the defect-related dI/dVb features are notsensitive to external Vg, unlike to spectra relating to underlyinggraphene and its energy-band alignment with a graphite probe(Supplementary Fig. 8). As compared with the well-isolated estates in mWS2, however, the mid-gap states in mMoS2 extendmuch wider inside the energy gap, making the defect-relatedtunnel spectra more conspicuous. The enlarged dI/dVb in theempty state suggests that mMoS2 films are inclined to containmore sulfur vacancies than mWS2, and that some of the vacanciesare mobile enough to agglomerate into energetically stable line-type defects, as theoretically expected13 and experimentallyconfirmed with TEM analyses28. In an earlier STM and ourtheoretical calculations confirm that defect states of neutraldisulfur vacancies (VSVS), the simplest form of vacancy chainsin mMoS2, have e–e divacancy hybridized defect states that areextensively expanded inside the energy gap29.Assessing atomic defects of Se-based SC-mTMDs. Figure 3a andc, respectively, displays the dI/dVb from mWSe2 and mMoSe2planar devices. Note that tunnel dI/dVb structures in mWSe2are notably lacking around the valence band, and the peak at–2.05 eV and the location where tunnel spectra start deviatingfrom the graphene baseline are quite distant considering theSOC-split valence-band edges, ΔSO (WSe2)= 0.43 eV. We attri-bute these smooth dI/dVb evolutions to an augmented momen-tum mismatch of the tunneling electrons from the graphite probeto the mWSe2 film in this particular tunnel junction. As discussedin previous reports, tunneling spectra from vdW planar hetero-junctions are not only sensitive to the sample DOS at a givenenergy but also rely on the crystal momentum alignments ofthe tunnel probe (graphite) and the 2D layers of interest (SC-mTMD)30–33. When electrons with momentum kgp are injectedfrom the graphite probe to the available states of the SC-mTMDat kmTMD, momentum of the tunnel electrons relaxes by Δk||=|kmTMD – kgp|, which is then directly linked to the probability ofelectron tunneling. The absolute value of tunnel dI/dVb isdetermined by the tunneling decay constant T ≈ (2meΦb/ħ2+(Δk||)2)1/2, where Φb is the tunnel barrier and me is the effectivemass of tunnel electrons. Thus, a larger momentum mismatch(Δk||) of tunnel electrons results in weaker signals and a smallerdI/dVb in value. Graphite is naturally considered as the mosteffective tunneling probe for investigating the electronic struc-tures of graphene and SC-mTMDs since most of the interestingfeatures of 2D hexagonal lattice materials are confined to theelectronic structures around the K point, at which the Fermi levelof the graphite probe is precisely located34. Here, we need toassert that only parts of the Brillouin zones (BZ) of the graphiteprobe and SC-mTMDs become matched, even for perfectlyaligned planar junctions, because of the lattice mismatch betweengraphene and SC-TMDs (Supplementary Fig. 9). However, elec-tron tunneling through 2D vdW heterojunctions consisting oflayered materials with different lattice constants needs to considerextended BZs of the heterostructures and their varying equipo-tential surfaces depending on Vb. We find that both of which aresensitive to the misalignment angle of the junctions, and tun-neling probability becomes highest for perfectly aligned hetero-structures, which will be discussed in detail in coming literature.We fabricate a second type of mWSe2 tunnel device withcrystalline angles of top graphite and mWSe2 layers tightlyaligned in order to efficiently probe the electronic structuresaround K. As expected, dI/dVb around the valence-band edgebecomes enhanced in value in the tightly aligned device (solidorange line in Fig. 3a). Resonant tunnel features with negativedI/dVb (green circles in Fig. 3a) confirm that the crystalline anglesof the graphite and mWSe2 are closely matched30–33. Bycomparing the dI/dVb from aligned and misaligned devices, weassign the upper edge of the SOC-split valence bands at –1.21 eV,and the lower SOC-split band edge to a dI/dVb crest at –1.64 eV,guided by optically determined ΔSO (mWSe2)= 0.43 eV. The dI/dVb peak at –2.05 eV is subsequently designated as the valence-band maximum at Γ.It is interesting to note that tunnel signals from the tightlyaligned device in the vicinity of the conduction-band edge differfrom the amplified dI/dVb around the valence band: dI/dVb at≈1.35 eV are not amplified as much as those around the valence-band maximum at K. Instead, a couple dI/dVb peaks becomeconspicuous at 1.50 eV and 1.53 eV in the tightly aligned sample,leading us to assign them as the SOC-split conduction-bandminima at the K point, and the band edge at 1.35 eV to theconduction-band minimum at Q (Supplementary Fig. 10). Withthese assignments, we assert that mWSe2 is an indirect bandgapand weakly doped p-type semiconductor, whose quasiparticleenergy gap is as large as Eg= 2.56 eV and exciton-binding energyEB= 0.82 eV (Eopt= 1.724 eV)15,27. Furthermore, SOC-split con-duction bands at K are found to be ΔSO,C (mWSe2)= 0.03 eV.Recently, Wang et al. reported the similar value (ΔSO,C(mWSe2) ≈ 0.04 eV) by optical reflectance and PL spectroscopymeasurements35.NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-11751-3 ARTICLENATURE COMMUNICATIONS |         (2019) 10:3825 | https://doi.org/10.1038/s41467-019-11751-3 | www.nature.com/naturecommunications 5www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsAlthough the rather moderate dI/dVb progression of themMoSe2 film is similar to the spectrum from the misalignedmWSe2 device, a tunnel feature corresponding to the SOC-splitlower valence-band edge at K is readily identified at –1.79 eV inboth regular and normalized dI/dVb (Fig. 3c). Consequently, thehigher SOC-split valence-band edge can be assigned at –1.59 eVbased on the optically obtained ΔSO (mMoSe2)= 0.20 eV, and thedI/dVb crest at –2.13 eV marks the valence-band maximum at Γ.Notably, the mMoSe2 spectra in the empty states are significantlyenhanced in value similar to the mMoS2, and dI/dVb becomesrealigned to the graphene baseline at ≈0.8 eV with a sizableadjustment of tunneling constant (dotted green line in Fig. 3c).We assign the conduction-band minimum of the mMoSe2 at0.87 eV, which makes mMoSe2 a direct bandgap n-typesemiconductor with a quasiparticle energy gap Eg= 2.46 eV andan exciton-binding energy EB= 0.82 eV (Eopt= 1.638 eV).The most common atomic defects in mWSe2 and mMoSe2films are selenium-atom vacancies12. Similar to the sulfurvacancies in mWS2 and mMoS2, singlet a1 states are expectedto form closer to the valence bands with varying spectral locationsin the Se-based TMDs; a1 states in mWSe2 mostly form below thevalence-band maximum, while the bulk portion of mMoSe2 a1defect states are expected to form inside the energy gap.Augmented dI/dVb attributed to the a1 defect states are delineatedin purple in Fig. 3a and c, where the a1 defect states in mMoSe2extend further inside the energy gap while the area relating to themWSe2 a1 defect states is apparently narrower. Doublet e defectstates from the missing selenium atoms are expected to form mid-gap states inside the energy gaps, with corresponding tunnelspectra of mWSe2 identified from the dI/dVb bumps inside theenergy gap (red arrows in Fig. 3a, Supplementary Fig. 8). Theamplified and extended dI/dVb of mMoSe2, over which the edefect states are known to exist, suggest that selenium vacanciesare more prevalent in mMoSe2 than mWSe2, and some of themtend to form vacancy chains or clusters.Comparison of the atomic defect states in SC-mTMDs. Wenumerically calculate the atomic defect DOS from chalcogen-atom vacancies in the four SC-mTMDs with a consideration ofthe SOC effect, and present overlaid plots with experimental datain Fig. 4a. In these calculations, we do not consider Coulombicmany-body effects since a rather simplified DFT is sufficientenough to explain the atomic defect states in SC-mTMDs. It iscrucial to note that the SOC effect influences not only theintrinsic electronic structures but also the defect states fromchalcogen-atom vacancies36. As displayed in Fig. 4a, the SOCeffect splits e defect states by ≈0.2 eV in mWS2 and mWSe2, while2.0 1.5 1.0 0.5 0.0 –0.5 –1.0 –1.5a bc d(± 0.01 eV)KQCBMVBMKΓ–1.21 eV–2.05 eV1.56 eVV1.53 eV1.35 eV–2.13 eV0.87 eV1.17 eV1.42 eV–1.59 eVKQCBMVBMKΓ10–510–610–710–810–910–1010–11dI/dVb (S)10–510–610–710–810–910–1010–11dI/dVb (S)ΔSOΔΓ-KΔΓ-KEg = 2.56 eVEg = 2.46 eV–1.64 eeV–1.79 eV1.00 eVeV–1.50 eEFEFmWSe2ΔQ-KΔQ-KΔSO,CΔSOVb (V)2.5 2.0 1.5 1.0 0.5 0.0 –0.5 –1.0 –1.5Vb (V)mMoSe2Normalized dI/dVb10020304050Normalized dI/dVb10020304050ΔQ-K = 0.15 eVΔQ-K = 0.13 eVΔSO,C = 0.03 eVEB = 0.82 eVEB = 0.82 eVEg = 2.56 eVEopt = 1.724 eVEopt = 1.638 eVΔSO,V = 0.43 eVΔSO = 0.20 eVΔΓ-K = 0.86 eVΔΓ-K = 0.54 eVEv = 1.21 eVEv = 1.59 eVEc = 1.35 eVEg = 2.46 eVEc = 0.87 eVEFEFmWSe2mMoSe2Fig. 3 Detailed electronic structure analyses from electron tunneling spectroscopy measurements of Se-based mTMDs. a, c Tunnel spectra plotted withdI/dVb in log scale from the mWSe2 (a) and mMoSe2 (c) planar tunnel junctions. Tunnel spectra from the crystallographically aligned device are delineatedwith solid orange lines, and negative dI/dVb features for resonant tunneling are marked with green circles. Solid and dotted green lines indicate thegraphene baseline spectra. The areas delineated with purple and orange, respectively, represent the a1 and e defect states from selenium-atom vacancies.b, d Summarized energy-level assignments for the mWSe2 (b) and mMoSe2 (d) films. Uncertainty for each energy-level assignment is less than ±0.01 eVARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-11751-36 NATURE COMMUNICATIONS |         (2019) 10:3825 | https://doi.org/10.1038/s41467-019-11751-3 | www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsthe splitting is minimal in mMoS2 and mMoSe2 (SupplementaryFig. 11). As experimentally and theoretically confirmed, the a1defect states of the Mo-based films extend further into the energygap, while the majority of the a1 states of the W-based films hideunder the valence bands. Spectral locations of the doublet e defectstates in mWS2 and mWSe2 are close to the theoretical expecta-tions, and calculated e states in mMoS2 and mMoSe2 are in thevicinity of the expanded defect-induced dI/dVb. We additionallycalculate the defect DOS by double chalcogen-atom vacancies(VSVS or VSeVSe) and present them with dotted gray lines in Fig. 4a.As noted previously, the e–e divacancy defects become hybridizedand form additional mid-gap states inside the energy gap,further extended toward the conduction-band edge in SC-mTMDs. We consider charge neutral chalcogen-atom vacanciesin our calculations, and find that the calculated spectral locationsof both a1 and e states in mMoS2, mMoSe2, and mWS2 films areconsistently shifted to lower energies than the experimentallyidentified positions, with the sole exception being the e defects inthe weakly p-doped mWSe2. Such consistent energy-level shiftingof a1 and e defect states to higher energies (toward conductionbands) presents a strong experimental implication thatchalcogen-atom vacancies in SC-mTMDs can work as dopants,especially as dominant donor states in mWS2, mMoS2, andmMoSe2 films.Here, it is worth mentioning that there could exist several otherdefects in the SC-mTMDs, such as H2 or N2 adatoms, transitionmetal-atom vacancies, or others. However, experimental identi-fications of such scant defects are daunting, especially in ourplanar junctions where active areas are as large as several micronsin dimension. The observed mid-gap states are ensembles of allthe available defects, whose spectra could be easily overshadowedby the more abundant defect sources; missing chalcogen atoms inS-based and Se-based SC-mTMDs. Moreover, the formationenergies of chalcogen-atom vacancies are favorable to many otherdefects. For example, much higher formation energies oftransition-metal-atom vacancies suggest that the missingtransition-metal atoms are not energetically favorable tochalcogen-atom vacancies, not to mention that the spectrallocations of such defects are different in energy from those ofchalcogen-atom vacancies (Supplementary Fig. 12)8,11,37,38. Inaddition, we find that the binding energies of H on SC-TMDs arenegative with respect to free H2 molecules; –1.9, –2.1, –2.2, and–2.4 eV/H, respectively, for MoS2, MoSe2, WS2, and WSe2, assimilar to N2 chemisorption37,38, suggesting that H atoms aremore likely to desorb from the TMDs and form H2 moleculesinstead. The calculated binding energies of H2 on the surface ofTMD films are a few tens of meV, which allow H2 to be easilydetached from the SC-TMD films as well.To further clarify the similarities and dissimilarities regardingatomic defect states in SC-mTMDs, we calculate the formationenergies (EVS,VSe) of individual chalcogen-atom vacancies in thefour films (Fig. 4b). Our calculations suggest that sulfur atoms arerelatively easier to be taken off with lower atomic-defectformation energies than selenium atoms, implying that mMoS2(EVS (mMoS2)= 1.267 eV) would have the most chalcogen-atomvacancies in total, while mWSe2 (EVSe (mWSe2)= 1.668 eV)would be the least vulnerable to losing selenium atoms. Moreover,we can deduce the density of states of chalcogen-atom vacanciesin the intrinsic SC-mTMDs, revealing that mMoS2 has the highestdefect DOS with DVS (mMoS2)= 1.46 × 1012 cm−2, followed bymWS2 (DVS (mWS2)= 6.95 × 1011 cm−2), mMoSe2 (DVS(mMoSe2)= 3.51 × 1011 cm−2), and finally mWSe2 with thelowest DOS at DVS (mWSe2)= 1.31 × 1011 cm−2.Intriguingly, tunneling spectra related to the doublet e defectstates in mWS2 remain as an isolated dI/dVb hump (Fig. 2a),despite the fact that mWS2 layers are expected to have a largerdefect DOS than mMoSe2, in which a much extended defect-induced dI/dVb bump is formed (Fig. 3c). Our DFT calculationsconfirm that sulfur vacancies in mWS2 films are the least likely tohybridize to form divacancies or vacancy chains, since thevacancy binding energy of mWS2 is the lowest (Ebind (mWS2)=0.033 eV) among the four films (Fig. 4c). In comparison,selenium-atom vacancies in mMoSe2, with a vacancy bindingenergy (Ebind (mMoSe2)= 0.126 eV) one order higher thanmWS2, are expected to form line-type defects or defect clusterswith relative ease, leading the mid-gap spectra originating fromdoublet e defect states to extend wider within the energy gap.Finally, a few dI/dVb humps for the doublet defect states in themWSe2 (Fig. 3a) could imply that some selenium-atom vacanciesbecome hybridized, justified by a relatively high vacancy binding–0.8 –0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4E–EVBM (eV)0.020.040.060.080.100.12e (sim.) e (sim.) EVBM ECBM1.21.31.41.51.61.7EVS,VSe (eV)Ebind (eV)bamWS 2mMoS2mWSe 2mMoSe 2mWS 2mMoS2mWSe 2mMoSe 2c1.396 eV1.267 eV1.668 eV1.499 eV0.033 eV0.068 eV0.086 eV0.126 eVmWS2mMoS2mWSe2mMoSe2VS, e (sim.)e (exp.)e (exp.)e (sim.)e (exp.)a1 (sim.)a1 (exp.)a1 (exp.)a1 (sim.)e (exp.)Defect density of states (DOS)VSVSVSVSVSeVSeVSeVSeFig. 4 DFT studies on chalcogen-atom vacancies in SC-mTMDs. a DFT-calculated locations and density of states of charge neutral a1 and e defect-states from single chalcogen-atom vacancies in the four SC-mTMD filmswith a consideration of the SOC effect. The defect DOS induced by doublechalcogen-atom vacancies are overlaid with dotted gray lines. Tops of thevalence-band edges are set at 0 eV. Note that quasiparticle energy gapsfrom DFT calculations are severely underestimated without theconsideration of electron–electron interactions. Experimentally identified a1and e defect states are, respectively, overlaid with brown and orangeshadows. b, c Formation (EVS,VSe, b) and binding (Ebind, c) energies ofindividual chalcogen-atom vacancies in the four representative filmsNATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-11751-3 ARTICLENATURE COMMUNICATIONS |         (2019) 10:3825 | https://doi.org/10.1038/s41467-019-11751-3 | www.nature.com/naturecommunications 7www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsenergy (Ebind (mWSe2)= 0.086 eV), although the overall numberof selenium-atom vacancies is expected to be the lowest amongthe four SC-mTMDs. However, we should note that these dI/dVbbumps could be also attributed to the SOC-induced defect-statesplittings, not just the double Se vacancies. At this moment, wecannot say with certainty whether the SOC or divacancy defectsor both are the sources for the isolated set of dI/dVb bumps inmWSe2, which calls for further theoretical and experimentalworks.DiscussionBy implementing electron tunneling and optical spectroscopymeasurements with DFT analyses, we have provided the mostaccurate and reliable material parameters to date of four repre-sentative SC-mTMD films. Specifically, our work includes spectraprofiles of the mid-gap states from individual chalcogen-atomvacancies, quasiparticle energy gaps, and exciton-binding ener-gies; all observed key material parameters are summarized in theTable 1. Through such experimental and theoretical studies, weare able to confirm that chalcogen-atom vacancies are the mostprevalent atomic defects in SC-mTMDs, and these defects inducetwo mid-gap states around valence band edges (singlet a1 states)and inside energy gaps (doublet e states). Atomic defect statesreveal similarities and dissimilarities among these four distinctiveSC-mTMDs regarding the spectral locations of the defect-inducedmid-gap states, physical vacancy formations, and intrinsic defectDOS. Our studies reveal that S-based mTMDs are more vulner-able to chalcogen-atom vacancies than their Se-based counter-parts, presenting strong experimental implications that suchvacancies are directly related to charged dopings in SC-mTMDs:S-based films are heavily doped n-type semiconductors, while Se-based films configure either as a moderately doped n-typesemiconductor (mMoSe2) or a weakly doped p-type (or intrinsic)semiconductor (mWSe2). Competing with the overall defect DOSand vacancy binding energies, chalcogen-atom vacancies in theintrinsic mMoS2, mMoSe2, and mWSe2 films are inclined to formhybridized vacancy chains while sulfur-atom vacancies in mWS2films remain isolated. In addition, we confirm that the energybands of the films are greatly renormalized by enhanced many-body interactions, and diminished screening effects in theatomically thin 2D structures, leading to exceptionally largeexcitonic-binding energies up to ≥0.78 eV. By implementingcrystalline angle-dependent electron-tunneling spectroscopies, wehave demonstrated that tunneling decay constants, and thereforetunnel signals in the 2D vdW heterostructures, can be readilytuned by controlling the tunnel-electron momentums betweentunnel probe and SC-mTMD crystals. This provides a usefulexperimental knob for investigating the electronic structures ofvarious TMDs with much improved measurement accuracy. Webelieve that the key material parameters presented in thisreport can provide a solid foundation for current and next-generation electronic and optical applications with ultrathinsemiconducting TMD films. Moreover, our experimentalapproaches can be applicable to any low-dimensional quantummaterials and their unlimited combinations for high-precisionmaterial metrology.MethodsDevice fabrication. In our planar vdW heterostructures, preparation of atomicallyclean interfaces is of critical importance for accurate and reliable material char-acterization of SC-mTMD films. At first, 60 -nm to 100- nm-thick high-crystallineh-BN flakes are mechanically exfoliated on a 90 -nm-thick SiO2 layer on Si sub-strate. Prior to exfoliation, we thoroughly clean the SiO2/Si substrates with acetoneand IPA in an ultrasonication bath and subsequent dipping in piranha solution.We carefully examine h-BN surface cleanness with a dark-filtered optical micro-scope to avoid cracks and nonuniform h-BN layers. Then, single-layer graphenemechanically isolated onto polymer stacks of PMMA (poly(methylmethacrylate))–PSS (polystyrene sulfonate) layers is transferred to the prelocatedh-BN flake on SiO2/Si substrate using a dry transfer method. The total thicknessesof PMMA and PSS films on bare Si substrates are adjusted for optimal opticalcontrasts to identify the layer number of graphene and tunnel h-BN. Once thePMMA/PSS/Si substrates with 2D layers of graphene, h-BN, SC-mTMDs, andgraphite on the polymer stacks are placed on top of DI water, the water soluble PSSlayer is quickly dissolved, and the PMMA layer with 2D materials becomes isolatedfrom the Si substrate. Then, with a micromanipulation stage equipped with arotator and an optical microscope, we transfer the 2D layers on PMMA to atargeted location on a SiO2/Si substrate with micrometer accuracy. After dissolvingPMMA in warm acetone (60 °C), we further anneal the samples in forming gases ofAr and H2 (9:1 ratio by flow rate). We set the annealing temperature at 350 °C forsingle-layer graphene and then reduce the temperature to 250 °C for SC-mTMDfilms to avoid undesired defect-state formations. After annealing, we confirm thesurface cleanness with an atomic force microscope. By following a similar drytransfer protocol, SC-mTMD films, thin h-BN (3–4 layers), and graphite flakes aresequentially transferred on top of the graphite-h-BN stack to complete the mTMD-based planar tunneling device. For the second type of planar tunnel devices, weintentionally align the crystalline angles of the top graphite and monolayer WSe2.No careful alignments are necessary for transferring thin tunnel h-BN andunderlying single-layer graphene films. Finally, titanium and gold (5 nm/95 nm)electrodes are fabricated to electrically connect the top graphite and bottom gra-phene layers by using standard electron-beam lithography and lift-off procedures.All four high-purity (>99.995%) SC-TMD crystals were purchased from HQGraphene with no additional dopants added during growth procedures.Electrical measurements. All electrical measurements are carried out under ahigh vacuum condition below 10−5 Torr with a cryogen-free probe station andcryogen-free dilution refrigerator, whose base temperatures are 5.7 K and below100 mK, respectively. We first characterize the electronic properties of ourplanar tunnel junctions with the probe station, and transfer the working devicesto the dilution refrigerator for further in-depth measurements. With SC-mTMDfilms encapsulated by noninteracting high-quality h-BN and graphene, ourdevices are resilient to multiple thermal circulations. Current–voltage character-istics of the mTMD planar tunnel junctions are measured with a DC voltagesource applied to the top graphite, and a current amplifier connected to thebottom graphene layer. Voltage output from the current amplifier is monitoredthrough a digital multimeter, and differential conductance (dI/dVb) is numericallyobtained.Optical measurements. Spectral information regarding the A-exciton peaks of theSC-mTMD films is measured with a micro-PL system pumped by a CW Nd: YAGlaser at 532 nm. Pump light is vertically shone onto the SC-mTMD flakes througha ×50 objective lens, and the PL signals collected through the same lens are ana-lyzed with a liquid nitrogen-cooled Si CCD detector with 550 -nm long pass filter.The spatial extent of the pump laser is confirmed to be 2 μm in diameter fromknife-edge experiments. Energy splitting between the A- and B-exciton peaks of theSC-mTMDs is measured with a micro-reflectance spectroscopy setup equippedwith a supercontinuum white light source. The diameter of the supercontinuumlight source is estimated to be 4 μm. For temperature-dependent PL and reflectancemeasurements, our mTMD-based planar junctions are mounted in a liquidnitrogen-cooled cryostat.DFT for atomic defect states. Density functional theory calculations are per-formed using the Vienna Ab initio Simulation Package (VASP)39. Ions arerepresented by projector-augmented wave (PAW) potentials40, and generalizedgradient approximation (PBE) is employed to describe the exchange-correlationfunctional41. A plane-wave basis set with an energy cutoff of 350 eV is employed todescribe electronic wave functions. For defect-state calculations, we use an 8 ×8 supercell with consideration of the dipole, and the Γ point for Brillouin-zoneintegration is used for structural optimizations and total energy calculations. Wefind that the effects from the dipole correction are very small, with an energyTable 1 Experimentally identified material parameters of thefour representative SC-mTMDsUnits: eVEg EV EC ΔSO ΔK-Γ(VB) ΔK-Q(CB) Eopt EBWS2 2.88 1.95 0.93 0.38 0.26 0.12 2.051 0.83MoS2 2.72 1.86 0.86 0.15 0.15 0.15 1.936 0.78WSe2 2.56 1.21 1.35 0.43 0.86 −0.15 1.724 0.82MoSe2 2.46 1.59 0.87 0.20 0.54 0.13 1.638 0.82All parameters listed are experimentally addressed by electron tunneling and opticalspectroscopy measurements with SC-mTMD-based planar heterostructures. Energy-levelassignments have uncertainty levels < ± 0.01 eVARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-11751-38 NATURE COMMUNICATIONS |         (2019) 10:3825 | https://doi.org/10.1038/s41467-019-11751-3 | www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsdifference of <1 meV for mMoS2 (Supplementary Fig. 12). The calculated hex-agonal lattice constants of mMoS2, mMoSe2, mWS2, and mWSe2 are 3.188 Å,3.312 Å, 3.179 Å, and 3.325 Å, respectively. The atomic positions of all clusters arerelaxed with residual forces smaller than 0.01 eV/Å.Data availabilityAll data supporting the findings of this study are available from the correspondingauthors on request.Received: 7 February 2019 Accepted: 5 August 2019References1. Srivastava, A. et al. Optically active quantum dots in monolayer WSe2. Nat.Nanotechnol. 10, 491–496 (2015).2. He, Y.-M. et al. Single quantum emitters in monolayer semiconductors. Nat.Nanotechnol. 10, 497–502 (2015).3. 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Lett. 77, 3865–3868 (1996).AcknowledgementsThis work was supported by a research grant for the Development of ConvergingMeasurement Technology for Nanotechnology (KRISS-2018-GP2018–0019) funded bythe Korea Research Institute of Standards and Science. This work was also supported bythe Basic Science Research Program (NRF-2016R1A2B4008816 and NRF-2019R1A2C2004007) through the National Research Foundations of Korea.Author contributionsT.Y.J., H.K., and S.J. fabricated devices and performed electron tunneling spectroscopymeasurements. T.Y.J. and K.J.Y. carried out optical spectroscopy measurements, S.-J.C.established an electron tunneling model of vertical 2D vdW heterostructures, and Y.-S.K.performed DFT calculations. High-quality h-BN crystals were synthesized by K.W. andT.T. T.Y.J., H.K., K.J.Y., S-J.C., Y.-S.K., and S.J. contributed in analyzing the data andpreparing the paper.Additional informationSupplementary Information accompanies this paper at https://doi.org/10.1038/s41467-019-11751-3.Competing interests: The authors declare no competing interests.Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/Peer review information: Nature Communications thanks Thomas Brumme and theother anonymous reviewer(s) for their contribution to the peer review of this work. Peerreviewer reports are available.Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-11751-3 ARTICLENATURE COMMUNICATIONS |         (2019) 10:3825 | https://doi.org/10.1038/s41467-019-11751-3 | www.nature.com/naturecommunications 9https://arxiv.org/abs/1810.02896https://arxiv.org/abs/1810.02896https://doi.org/10.1038/s41467-019-11751-3https://doi.org/10.1038/s41467-019-11751-3http://npg.nature.com/reprintsandpermissions/http://npg.nature.com/reprintsandpermissions/www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsOpen Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directly fromthe copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2019ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-11751-310 NATURE COMMUNICATIONS |         (2019) 10:3825 | https://doi.org/10.1038/s41467-019-11751-3 | www.nature.com/naturecommunicationshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.nature.com/naturecommunications Spectroscopic studies of atomic defects and bandgap renormalization in semiconducting monolayer transition metal dichalcogenides Results 2D vdW planar tunnel junctions with SC-mTMDs Electron tunneling and optical spectroscopy measurements Assessing atomic defects of S-based SC-mTMDs Assessing atomic defects of Se-based SC-mTMDs Comparison of the atomic defect states in SC-mTMDs Discussion Methods Device fabrication Electrical measurements Optical measurements DFT for atomic defect states Data availability References Acknowledgements Author contributions Additional information