Introduction

As layered two-dimensional (2D) materials, transition metal dichalcogenides (TMDs) have attracted intense interest owing to their unique properties that are potentially advantageous for applications in wide areas1,2,3. Molybdenum disulfide (MoS2) is an archetypal TMD material with potential in electronic4,5,6, optoelectronic7,8, photovoltaic9,10, catalytic11,12, and sensing13 applications. Since the successful realization of field-effect transistor (FET) devices using a single or few MoS2 layer channel4, considerable research has focused on high-performance and novel electronic and optoelectronic devices using various 2D materials14,15,16. The device performance is affected by intrinsic factors (quality of the materials with defects, including structural imperfections and unintentional impurities) and extrinsic factors (doping from substrates and surface adsorbates, metal-semiconductor junction causing a Schottky barrier). Extensive efforts have been devoted to enhancing the device’s performance, focusing mainly on extrinsic factors. Notable progress has been made, for example, through encapsulation17, dielectric interface engineering18, and reduction of the Schottky barrier height19. It is also important to improve the inherent properties of MoS2, which are determined by intrinsic factors. As a first step, it is essential to clarify the carrier type and work function (WF) and identify the defects present in natural or grown MoS2. Such basic knowledge can be exploited to fabricate high-performance devices.

Most MoS2 FETs exhibit n-type transport behavior4,5,6,7,13,20,21,22,23, while ambipolar transport was also reported in some studies24,25. The band structure of MoS2 measured using angle-resolved photoemission spectroscopy (ARPES) showed unanimously that the valence band is located well below the Fermi level (EF) (>1 eV)26,27,28,29,30. These have led to the speculation that natural MoS2 without intentional doping is an n-type semiconductor. The intrinsic n-type MoS2 was often attributed to S vacancies, which were believed to be the most abundant and probable defects in MoS2 owing to its small formation energy31,32,33,34. On the other hand, the role of S vacancies as electron donors was not supported by most theoretical studies35,36,37,38. Other impurities, such as Cl or Br7, Re36, and H38, have been suggested as alternative causes of n-type doping. Scanning tunneling microscopy (STM) studies have shown that S vacancies and other defects are present near the MoS2 surfaces33,39,40,41. These near-surface defects were postulated to act as unintended dopants, but their nature has not been identified. Therefore, identifying these intrinsic defects in MoS2 remains elusive, and a consistent understanding of the origin of the predominantly observed n-type properties is lacking.

Here, we present evidence that n-type doping of MoS2 is provided by carbon (C) atoms through studies combining photoemission spectroscopy (PES), STM, and density-functional theory (DFT) calculations. ARPES data have shown that the EF of the newly exfoliated MoS2 is located near the valence band maximum (VBM) when C atoms are not detected. As the amount of C increases over time, the EF gradually moves away from the VBM with a concurrent decrease in the WF, indicating that the C impurity induces a change in doping from p- to n-type. STM showed that the nanometer-scale defects commonly observed on MoS2 surfaces increased in number over time, indicating their correlation with C atoms. All these experimental observations correlated to the increasing amounts of C were confirmed by intentionally depositing C atoms on the MoS2 surface. DFT calculations corroborated the C-induced doping change from p- to n-type and the WF variation. Theoretical results also suggest that the initial p-type doping observed in the absence of carbon is attributed to S vacancies at the surface.

Result and discussion

Angle-resolved photoemission spectroscopy

Although MoS2 is one of the representative 2D layered materials, it has a sizable band dispersion (as much as 0.5 eV) in the direction perpendicular to the layers due to interlayer coupling42. Therefore, it is crucial to use the appropriate photon energy (56 eV) to determine the VBM accurately when measuring the in-plane band structure (Supplementary Fig. 1). Figure 1a shows experimental band structures measured immediately after exfoliation in ultra-high vacuum (UHV) for representative MoS2 samples (samples-A1 and A2). Many of the investigated samples showed similar data, and overall features (including the VBM at approximately −0.7 to −0.9 eV relative to EF) are in good agreement with previous results26,27,28,29,30. For some freshly exfoliated samples [sample-B in Fig. 1b], ARPES data show rigid energy shifts with a similar band structure to those of Fig. 1a. The exact VBM was determined after taking the constant energy map (Supplementary Fig. 2). The VBM located at −0.2 eV is very close to the EF, which is very unusual. Considering the bulk band gap of 1.2–1.3 eV, samples-A1 and A2 and sample-B are n- and p-type semiconductors, respectively, exhibiting the variability of MoS2 in doping. Sample-B, being initially p-type, showed a shift of the VBM to higher binding energy (i.e., a shift of EF upward from the VBM) with time [Fig. 1b–d]. The VBM shifted down by ~0.7 eV after 24 h of aging under UHV without any treatment. After 48 h of aging, the VBM was lowered further, reaching ~−1.1 eV. This indicates that a change in the doping type of the MoS2 toward n-type occurs over time. In order to prove the reproducibility, we tested a number of pristine-MoS2 samples. About 20–30% of them showed p-type properties, and the others presented n-type properties depending on the carbon amount. In addition to the change in the VBM, the measured WF also changed over time. The WF of sample-B (5.8 eV) was initially larger than those of the freshly exfoliated samples-A1 and A2 (WF = 5.2–5.5 eV). However, the WF of sample-B decreased with time and reached 4.9 eV after 48 h, similar to the typical value for the n-type MoS2. High-resolution core-level PES was used to explain the differences in VBM and WF between different MoS2 samples [insets of Fig. 1a–d and Supplementary Fig. 3]. When the carbon-free sample was kept in the UHV chamber for a long time, the C 1 s peak began to appear and grew slowly over time [insets of Fig. 1c, d, and Supplementary Fig. 3b]. We also investigated the possible adsorption of other adsorbates, such as O2 and H2O. Wide spectra taken over time with a photon energy of 630 eV confirm that no other adsorbates are detected except for C (Supplementary Fig. 4).

Fig. 1: ARPES and PES spectra with different samples.
figure 1

a ARPES data showing electronic band structures for different MoS2 samples. Samples-A1 and A2 with noticeable amounts of carbon were obtained immediately after exfoliation in the UHV of 1.3 × 10−10 Torr. b Another sample-B with a small amount of carbon immediately after exfoliation under UHV, c after 24 h, and d after 48 h. ARPES data were taken at the photon energy of 56 eV along the Γ-K symmetry direction of the surface Brillouin zone. The color scales in the figures are the same. Insets show C 1s PES spectra corresponding to the ARPES data. e Relative peak intensity of C 1s to S 2p (IC1s/IS2p) for samples-A1, A2, and B with time. f VBM of MoS2 as a function of IC1s/IS2p. g WF of MoS2 as a function of IC1s/IS2p.

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Figure 1e plots the C1s/S2p peak intensity ratio (IC1s/IS2p) as a function of time for sample-B (data for the as-exfoliated samples-A1, A2 are also shown). Figure 1f, g shows the observed VBM and the WF as functions of IC1s/IS2p, respectively. The strong dependence on the carbon content is evident, suggesting that the carbon is responsible for the time-dependent changes in the electronic properties. The correlation of the time-dependent changes in the VBM and the WF to the measured carbon content was well reproduced.

Carbon was deposited directly onto the MoS2 to clarify the origin of the time-dependent changes shown in Fig. 1. Figure 2a shows the band structure of a MoS2 containing trace amounts of carbon, where the VBM is very close to the EF. When carbon was deposited for 5, 10, 15, and 20-min [Fig. 2b–e], the VBM moved down relative to \({E}_{F}\). Finally, the VBM was lowered to −1.18 eV after 20-min deposition. The IC1s/IS2p in Fig. 2f shows that the amount of carbon increased with deposition time. Both the VBM [Fig. 2g] and WF [Fig. 2h] decreased almost linearly with increasing IC1s/IS2p. The results were entirely consistent with the observed aging-induced changes. This shows that carbon is the origin of the changes in the VBM and WF.

Fig. 2: ARPES with increasing carbon amounts.
figure 2

a–e Evolution of electronic band structures of the as-exfoliated MoS2 (sample-C) with increasing carbon deposition. f IC1s/IS2p as a function of the carbon deposition time. g VBM of the MoS2 as a function of IC1s/IS2p. h WF of the MoS2 as a function of IC1s/IS2p.

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Scanning tunneling microscopy

Figure 3 shows STM images of MoS2. Several point defects are shown in the freshly exfoliated surface [Fig. 3a]. These defects are a few nanometers in size and are distinct from S vacancies that appear on the atomic scale (Supplementary Fig. 5). Two types of nanometer-scale defects could be distinguished at negative sample bias (i.e., in filled-state image): one appearing as bright elevations and the other as dark depressions [inset of Fig. 3b]. Both defects appear dark and are almost indistinguishable at positive sample bias (not shown). These nanometer-scale defects increased in number over time, as shown in a representative image of the MoS2 surface obtained after 10 days [Fig. 3b]. No other new defects were observed. Previous STM studies also reported observations of these nanometer-scale defects commonly present on MoS2 surfaces32,33,34,39,40,41. In some studies, these defects have been attributed to S-vacancies32,33. On the other hand, S vacancies were imaged independently as atomic-scale features40,43 (Supplementary Fig. 6). Thus, the observed nanometer-scale defects cannot be S vacancies, and their origin is still unknown. Considering that the amount of C in the PES data increased with aging, the nanometer-scale defects in STM images could be attributed to C-related features. Therefore, the MoS2 surface was also investigated after C atoms were deposited to test the C-related origin of the nanometer-scale defects observed in STM images. Figure 3c–e shows the change in the MoS2 surface with increasing C deposition (deposition time is changed while the other deposition parameters are fixed). The C-deposited surface exhibited the same nanometer-scale defects as those observed on the as-exfoliated and the aged surfaces [inset of Fig. 3d]. No other new defect features were observed. The number of “bright” (B) and “dark” (D) defect features in the filled-state image increased with increasing C deposition time [Fig. 3f], suggesting that both defects are related to C atoms. The consistency between aging and C-deposited samples clearly shows that nanometer-scale defects commonly observed on MoS2 surfaces originate from C atoms.

Fig. 3: STM images.
figure 3

STM images of aging effect: as-exfoliated (a) and after 10 days of aging (b). Effect of C deposition with varying deposition time: 0 min (as-exfoliated) (c), 10 min (d), and 30 min (e). All scale bars are 40 nm in (a–e), 4 nm for insets of (b) and (d). f The number of defects imaged per frame as a function of the C deposition time. Images were obtained with Vs = −1.0 V and It = 0.3 nA. Insets in (b) and (d) are zoomed-in images (Vs = −1.0 V and It = 0.1 nA) showing the bright (B) and dark (D) defects. The defects that appeared with aging and after C deposition are the same.

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In many studies, the almost universal n-type characteristics of the MoS2 materials and transistor devices based on them were attributed to S vacancies. This widely held belief originates from the consideration that the intrinsic S vacancies are prevalent on the surface because of their small formation energy. With the same reasoning, the nanometer-scale defects observed frequently in STM images were often interpreted as S vacancies with one or a few missing S atoms32,33,34. On the other hand, the present study showed that the nanometer-scale defects are clearly distinguished from S vacancies, which is consistent with a recent study40. Indeed, those defects are closely related to C impurities.

Density-functional theory calculations

DFT calculations were performed to investigate the origin of the carbon-induced n-type doping behavior of MoS2. In addition to the native S vacancy (VS), atomic C impurities at the surface were considered, such as the S-substituting C defect (CS) and the interstitial C defects. Figure 4a shows the local atomic structures around VS, CS, and two interstitial C defects (Cint and C’int), as well as the pristine (i.e., defect-free) case. Cint resembles a CS dimer substituting an S atom, whereas C’int involves a C atom at the hollow site above Mo. Cint was found to be the lowest energy structure among all the interstitial defects we considered, which include metastable structures with C residing within the van der Waals (vdW) gap (Supplementary Fig. 6). Figure 4b shows the band structures, where all the energy levels are relative to VBM. The pristine band structure shows an indirect band gap, and the EF is set to the midgap (0.62 eV above VBM). For VS, the nearly flat bands (blue symbols) caused by Mo dangling bonds appeared at −0.39 eV (occupied) and 0.81 eV (unoccupied). This shifts the EF (0.40 eV) closer to VBM compared with the pristine case, which is consistent with the literature35,36. Therefore, the MoS2 surface with VS exhibits p-type characteristics.

Fig. 4: DFT calculations.
figure 4

a Top and side views of pristine MoS2, defective ones with S vacancy (VS), S-substituting C defect (CS), and two interstitial C defects (Cint and C’int). Atomic defects are located at the outermost atomic layer. The bright purple, yellow, and red balls denote the Mo, S, and C atoms, respectively, while the three blue balls are Mo atoms adjacent to VS (indicated by the dashed circle). b Band structures of pristine and defective MoS2 bilayers using a 4 × 4 supercell. The horizontal dashed line indicates the EF set to be the center of the energy gap. The blue and red circles denote the major contributions of Mo atoms with the dangling bonds and C atoms, respectively. The solid and open circles indicate the occupied and unoccupied states, respectively. All the energy levels are aligned relative to the VBM for easy recognition of the EF shift.

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In the band structure of a surface with CS, the dangling bond states of Mo disappear, and an unoccupied C-induced gap state (red symbols) appears at approximately 0.70 eV. Therefore, the EF is lowered to 0.31 eV, exhibiting p-type behavior similar to VS. For the two interstitial C defects Cint (C’int), two C-induced bands appeared: one occupied at ~0.4 (0.6) eV and the other unoccupied at ~1.2 (1.1) eV. The resulting EF at 0.80 (0.81) eV was raised toward CBM by about 0.18 (0.19) eV, compared with the pristine case. This suggests that both interstitial C defects Cint and C’int exhibit n-type behavior, which is different from the p-type behavior of VS and CS defects.

The WFs were calculated for the pristine and the defected MoS2 surfaces. The WF increased for VS (5.28 eV) and CS (5.37 eV) but decreased for Cint (4.88 eV) and C’int (4.87 eV) compared to the pristine surface (5.06 eV). The changes in the EF and the WF due to Cint and C’int are consistent with the C-induced changes observed in the ARPES experiments. Therefore, the p-type observed for freshly exfoliated MoS2 is attributed to VS and possibly to CS, and the carbon defects causing the n-type are ascribed to interstitial C. Two interstitial C (Cint and C’int) configurations are matched with the two experimental nanometer-scale defect types (B and D). However, we are not able to match which of the experimental defects corresponds to which theoretical interstitial C configurations due to the limited STM images and the difficulties of simulating such large-size defects.

Based on the theoretical calculations, we propose that S vacancies or S-substituting C atoms induce p-type behavior, accounting for the observed EF close to the VBM [Fig. 1b]. This proposition contradicts the prevailing belief that S vacancies are responsible for n-type behavior31,32,33,34. Whereas the supporting evidence showing that S vacancies induce p-type can also be found in previous studies. Several PES studies have reported the change in MoS2 from n- to p-type upon thermal annealing44,45 and ion irradiation46,47. Because S vacancies are expected to be generated in those processes, the n- to p-type change was correlated with S vacancies. Previous STM and scanning tunneling spectroscopy (STS) data obtained near atomic-scale defects, considered neutral S-vacancy defects, showed the EF close to the VBM, which is indicative of p-type. All these previous studies support the proposition that S vacancies (S-substituting C atoms) induce p-type properties rather than n-type properties. The change from p- to n-type is due to the near-surface C impurities (interstitial C), which increase in amount over time.

A previous study has reported that as-exfoliated MoS2 surfaces exhibit almost intrinsic properties, whereas surface electron accumulation (SEA) occurs upon prolonged exposure to air48. STS and ARPES data indicated a shift in the EF toward the conduction band in the aged samples, which is consistent with SEA. The authors attributed the SEA to the formation of S vacancies caused by a slow desulfurization process based on the unsubstantiated correlation between the prevailing n-type behavior and the expected predominance of S vacancies. On the other hand, our experimental observations and theoretical calculations clearly show that the change from p- to n-type is due to near-surface C impurities. Evidently, the C impurities (interstitial C) are the origin of the universally observed n-type properties of the MoS2. Note that there was an older publication reporting a decrease in electron affinity and ionization potential with surface contamination by C49, which is consistent with the C origin of n-type MoS2 demonstrated in our study.

The remaining question to be answered is where the C impurity atoms originate. The C impurity was recently reported for another TMD, WS2 monolayer synthesized by chemical vapor deposition (CVD)50,51. In those studies, CH substituting for S atoms (CHS) was proposed as the most stable C-related point defect on monolayer WS2 in the plasma-enhanced CVD environment with methane gas. The possibility of the external origin of the C-related impurities on our MoS2 from residual C-containing molecules in UHV was tested by dosing C2H2 and CO gases. Despite the significant amounts of dosing, C2H2 resulted in no changes in the band structure, whereas CO induced a slight downward shift of the VBM. However, the change was too small to account for the temporal changes (Supplementary Fig. 7). Note that the CHS defects on monolayer WS2 show similar nanometer-scale STM contrast to the B defects on MoS251. CH incorporation is a possible high-temperature process in hydrocarbon-containing environments, but since our experiments were not carried out in such environments, we rule out the possibility of the CHS as C-related defects on MoS2.

Our DFT calculations show that carbon atoms favor near-surface regions (Supplementary Fig. 8), so there exists a net thermodynamic driving force for outward C diffusion. The inner C atoms will diffuse mainly along paths whose energy barriers are relatively lower than others. We speculate the diffusion path consisting of (1) horizontal hoppings from one Cint site to neighboring Cint sites via C’int, (2) vertical hoppings across vdW gaps, and (3) penetrations through atomic (MoS2) layers. Our calculations of hopping barriers suggest that the vertical hopping across the vdW gap is much slower than the horizontal hopping (Supplementary Fig. 9). While C impurities hardly go through complete MoS2 layers, they will be able to cross each MoS2 layer through sufficiently large voids. Since chemically active sites around voids are more likely to be passivated, the associated penetration of C atoms is expected to be relatively easy. Therefore, we estimate the outward diffusion length to be of the order of sub-micrometer per one day at room temperature (RT) (see Supplementary Note 8). It matches reasonably well with the experimental time scale to observe an increased amount of C atoms.

The C atoms can exist in different configurations, Cint (or C’int) and CS, when the MoS2 sample contains VS defects. The calculated formation energies of considered defects indicate that a CS defect is more stable by 4.5 eV than coexisting single defects of VS and Cint. This implies that C impurity atoms tend to form CS defects by occupying the existing S vacancies. As discussed above, C impurity atoms would diffuse outward over time after exfoliation, whose form is likely to be Cint and change to CS by sitting down to VS near the surface at an early stage. The electronic band structure indicates that CS, like VS, exhibits p-type characteristics, which is in accordance with the observed p-type ARPES data for freshly exfoliated samples. Over time, all existing S vacancies are consumed. Then, additional out-diffusing C atoms inevitably constitute the less stable Cint defects that exhibit n-type properties. This is consistent with the ARPES observations of changes from p-type to n-type with aging. We also confirmed that the stable charge states are neutral in the significant portion of the range of EF for all the considered defects (Supplementary Fig. 10).

A question remains whether the carbon can be the origin of the n-type conductivity even in MoS2 FETs where monolayer and/or CVD-grown samples are used, and thus C diffusion from bulk is excluded. In these cases, we speculate that C impurities may be incorporated during or after synthesis in the process of transfer for the measurement or device fabrication.

In summary, we have shown that C atoms near the surface of MoS2 are responsible for the predominant n-type doping of natural minerals and the frequently observed nanometer-scale defects at the surface in STM images. Newly exfoliated MoS2 surfaces occasionally exhibit p-type behavior when C atoms are barely detected. The p-type MoS2 is due to S vacancies at the surface. The carbon-free p-type MoS2 changes to n-type over time with the simultaneous increase in the amounts of C. The carbon atoms are supposed to migrate from the bulk to the near-surface region, resulting in unintentional n-type doping of the MoS2 surface. The origin of the intrinsic p- and n-type doping of natural MoS2 disclosed in this study provides new prospects to control doping for electronic and optoelectronic applications.

Methods

Photoemission spectroscopy

Experiments were conducted using commercially available single-crystal 2H-MoS2 flakes, referred to as “pristine MoS2.” The pristine MoS2 crystals were exfoliated using the scotch-tape method in ultra-high vacuum (UHV) with pressures ranging from 10−8 to 10−10 Torr. After transferring the exfoliated sample to the analysis chamber, The PES data were measured at the 10D beamline of the Pohang Accelerator Laboratory (PAL), which is equipped with Scienta DA30, R4000, and PHOIBOS 150 analyzers. For the exfoliated surface, the valence band and the C 1s and O 1s core levels were measured. A photon energy of 56 eV was used for the valence band and WF measurements, and 360 and 650 eV for C 1s and O 1s peaks, respectively. The binding energies were calibrated by measuring the Au Fermi energy or Au 4f7/2 core-level peak depending on the photon energy. A bias voltage of −10 V with an uncertainty of ±0.01 V was applied to the samples for the WF measurements. All the photoemission data were collected at RT. A homemade C evaporator, where an electron beam hits a carbon rod (99.99%), was used for carbon deposition in the PES experiments.

Scanning tunneling microscopy

STM experiments were carried out in an independent UHV chamber with a base pressure <3.0 × 10−10 Torr. For the experiments, single-crystal flakes of natural MoS2 minerals mounted on pieces of a Si wafer were exfoliated using scotch tape in the UHV for in-situ measurements. The STM measurements were performed at RT using two STM instruments: a home-built STM and a commercial STM (SPECS Inc.). All STM images were taken in the constant current mode. The same e-beam C evaporator as in the PES experiments was used for carbon deposition in the STM experiments.

Density-functional theory calculations

Theoretical calculations were performed within the Vienna Ab-initio Simulation Package (VASP)52. The projector-augmented-wave pseudopotentials were used for the plane wave basis set for modeling the ion cores. The Perdew–Burke–Ernzerhof generalized gradient approximation was used for the exchange-correlation functional with the inclusion of spin polarization. The optB88-vdW van der Waals density-functional was used to describe the dispersion interactions in each system. A kinetic energy cutoff of 500 eV for the basis set and a 5 × 5 × 1 k-point mesh for the Brillouin zone integration were used for the 4 × 4 MoS2 bilayer supercell. All atomic structures were fully relaxed until the forces on each atom were less than 0.01 eV/Å.