Interface Structure and Doping of Chemical Vapor Deposition‐Grown MoS2 on 4H–SiC by Microscopic Analyses and Ab Initio Calculations

The interface structure and electronic properties of monolayer (1L) MoS2 domains grown by chemical vapor deposition on 4H–SiC(0001) are investigated by microscopic/spectroscopic analyses combined with ab initio calculations. The triangular domains are epitaxially oriented on the (0001) basal plane, with the presence of a van der Waals (vdW) gap between 1L–MoS2 and the SiC terraces. The high crystalline quality of the domains is confirmed by photoluminescence emission. Furthermore, a very low tensile strain (ε ≈ 0.03%) of 1L–MoS2, consistent with the small in‐plane lattice mismatch, and a p‐type doping of (0.45 ± 0.11) × 1013 cm−2, is evaluated by Raman mapping. Density functional theory (DFT) calculations of the MoS2/4H–SiC(0001) system are also performed, considering different levels of refinement of the model: 1) the simple case of the junction between Si‐terminated SiC and MoS2, showing a covalent bond between the Si–S atoms and n‐type doping of MoS2; 2) the complete passivation of Si dangling bonds with a monolayer (1 ML) of oxygen atoms, resulting in a vdW bond with dSi–S ≈ 3.84 Å bond length and p‐type doping of MoS2; and 3) partial (¼ ML and ½ ML) oxygen coverages of the 4H–SiC surface, resulting in intermediate values of dSi–S and doping behavior.


Introduction
Transition metal dichalcogenides (TMDs) are a class of 2D materials described by the general formula MX 2 , where M are transition metal atoms (Mo,W,.)and X is a chalcogen (S, Se, and Te).TMDs are featured by strong in-plane bonds between the constituent atoms (X-M-X) and weak van der Waals (vdW) interactions between the stacked layers. [1]Molybdenum disulfide (MoS 2 ) is the most investigated among TMDs, due to its abundance in nature and the chemical stability at room temperature.In particular, the 2H-MoS 2 semiconductor phase exhibits a tunable bandgap as a function of the thickness, with a transition from an indirect bandgap of 1.2 eV for few-layer MoS 2 to a direct bandgap of 1.8-1.9eV for monolayer (1L) MoS 2 . [2,3][6][7] Furthermore, its dangling bonds free surface provides the opportunity to fabricate vdW heterostructures both in combination with other 2D materials (2D/2D heterostructures) and with bulk semiconductors (2D/3D semiconductor heterostructures). [8,9]In this context, significant research efforts have been recently directed on the integration of the MoS 2 with wide-bandgap (WBG) semiconductors, such as silicon carbide (4H-and 6H-SiC), gallium nitride (GaN), and related group-III nitrides (AlN and AlGaN alloys), with the aim of The interface structure and electronic properties of monolayer (1L) MoS 2 domains grown by chemical vapor deposition on 4H-SiC(0001) are investigated by microscopic/spectroscopic analyses combined with ab initio calculations.The triangular domains are epitaxially oriented on the (0001) basal plane, with the presence of a van der Waals (vdW) gap between 1L-MoS 2 and the SiC terraces.The high crystalline quality of the domains is confirmed by photoluminescence emission.Furthermore, a very low tensile strain (ε % 0.03%) of 1L-MoS 2 , consistent with the small in-plane lattice mismatch, and a p-type doping of (0.45 AE 0.11) Â 10 13 cm À2 , is evaluated by Raman mapping.Density functional theory (DFT) calculations of the MoS 2 /4H-SiC(0001) system are also performed, considering different levels of refinement of the model: 1) the simple case of the junction between Si-terminated SiC and MoS 2 , showing a covalent bond between the Si-S atoms and n-type doping of MoS 2 ; 2) the complete passivation of Si dangling bonds with a monolayer (1 ML) of oxygen atoms, resulting in a vdW bond with d Si-S % 3.84 Å bond length and p-type doping of MoS 2 ; and 3) partial (¼ ML and ½ ML) oxygen coverages of the 4H-SiC surface, resulting in intermediate values of d Si-S and doping behavior.
[16][17][18] The hexagonal structure of 4H-SiC and GaN and the very low lattice mismatch with MoS 2 on the basal plane (%2.9% in the case of 4H-SiC and < 1% in the case of GaN) favor the direct epitaxial growth of MoS 2 layers on these substrates.The nucleation and growth of highly oriented and nearly unstrained triangular MoS 2 domains are obtained on the GaN(0001) basal plane by chemical vapor deposition (CVD) at temperatures of 700-800 °C. [8]On the other hand, a large variety of MoS 2 configurations has been reported by CVD on the surface of 6H-or 4H-SiC(0001) depending on the growth conditions and the SiC miscut angle (i.e., on-axis or off-axis surface).These include uniform planar films (suitable for electronic applications) [12] and vertically standing triangular flakes exposing MoS 2 edges (more suitable for catalytic applications). [19]In the case of planar MoS 2 on these SiC surfaces, studies of the early growth stages, providing information on the rotational alignment of MoS 2 domains with respect to the (0001) basal plane, are still missing and would be highly desirable.Furthermore, a deeper understanding of the interface bond, strain, and doping for CVD-grown MoS 2 on 4H-SiC(0001) is required, both by microscopic characterizations and ab initio calculations, to exploit the potentialities of this system for electronic applications.Recently, ab initio computational studies of the equilibrium configurations for 1L-MoS 2 heterostructures with the Si-terminated SiC(0001) surface have been reported, showing that the most energetically stable configuration is the one where S atoms are located on top of Si atoms with an equilibrium distance d Si-S = 2.21 Å. [20] Such a small d Si-S value indicates a strong (covalent-like) bond between MoS 2 and 4H-SiC(0001) in this idealized model of the heterostructure.In this context, further computational studies considering additional effects, such as the natural propensity of the Si-terminated 4H-SiC surface to be passivated by oxygen atoms, are required to provide a more realistic description of the 1L-MoS 2 /4H-SiC system.
In this article, we investigated the interface structure and electronic properties of CVD-grown 1L-MoS 2 on 4H-SiC(0001), by combining microscopic and spectroscopic analyses with density functional theory (DFT) calculations.High-crystalline-quality triangular domains, mostly composed of 1L-MoS 2, were obtained on the surface of 4H-SiC(0001) 4°off-cut samples by CVD with S and MoO 3 vapors at 700 °C.Top-view scanning electron microscopy (SEM) analyses showed preferential orientation of these domains along specific directions, indicating an epitaxial relation with the (0001) basal plane, while cross-sectional scanning transmission electron microscopy (STEM) measurements demonstrated a conformal coverage of 1L-MoS 2 on the SiC terraces, with a vdW gap in between.A very low tensile strain (ε % 0.03%) of 1L-MoS 2 , consistent with the very low in-plane lattice mismatch, and p-type doping of (0.45 AE 0.11) Â 10 13 cm À2 was evaluated by Raman analyses.To get an interpretation of these experimental results, DFT calculations of the equilibrium structure and electronic bands for the MoS 2 /4H-SiC(0001) system were also performed, considering different levels of refinement of the model: 1) the simple case of the junction between Si-terminated SiC and MoS 2 showing covalent bonds with d Si-S = 2.24 Å between the Si-S atoms and n-type doping of MoS 2 ; 2) the complete passivation of Si dangling bonds with a monolayer (1 ML) of oxygen atoms, resulting in a van der Waals bond with d Si-S % 3.84 Å and p-type doping of MoS 2 ; and 3) partial (¼ ML and ½ ML) oxygen coverage of the 4H-SiC surface, resulting in intermediate values of d Si-S and doping behavior.Interestingly, the complete O-passivation of the Si-terminated 4H-SiC surface caused a rehybridization of the underlying carbon atoms from sp 3 to sp 2 , which was found to be the origin of the p-type doping of 1L-MoS 2 .

Results
A representative in-plane SEM image of the as-grown MoS 2 on 4H-SiC (0001) by CVD is reported in Figure 1a, showing the formation of triangular flakes with a 100-300 nm lateral size.Most of these flakes exhibit two preferential orientations, as illustrated by the red triangles at 0°and 180°with respect to the reference dashed line in the figure, suggesting the epitaxial growth of MoS 2 on hexagonal SiC with a high degree of rotational alignment.This aspect has been confirmed by an accurate statistical analysis of domains orientation, carried out on all MoS 2 triangles in the SEM image.The result of this analysis, reported in the histogram of Figure 1b, shows that the grown MoS 2 domains are almost equally distributed in two groups with orientations of 0°AE 30°a nd 180°AE 30°.The rotational alignment of MoS 2 domains on 4H-SiC(0001) surface is beneficial for the reduction of grain boundaries in the continuous MoS 2 film formed by merging of the domains during longer CVD processes, as reported in previous works. [21,22]Figure 1c shows a cross-sectional STEM image collected in the high-angle-annular dark-field (HAADF) mode on one of these triangular domains.The intensity contrast in this imaging mode, related to the atomic number (Z ), allows to clearly identify materials with different density, that is, the SiC substrate, the deposited MoS 2 layer, and a carbon thin film capped with Pt (used to protect MoS 2 during the lamella preparation by focused ion beam).In particular, the presence of 1L-MoS 2 conformal to the stepped surface of 4 -offcut 4H-SiC, with a vdW gap in between, is clearly resolved from this microscopic analysis, as indicated in Figure 1c.
Besides the HAADF-STEM analysis, chemical mapping by EDS was performed on the same cross-sectioned sample, as reported in the Figure S1, Supporting Information.This analysis shows an evident accumulation (above the background signal) of oxygen on the SiC surface, below the MoS 2 layer.This observation supports the DFT model of oxygen passivation of SiC surface, discussed in the final part of this article.
The high crystalline quality and the monolayer thickness of the as-grown MoS 2 domains on 4H-SiC were also confirmed by the observation of photoluminescence (PL) spectra, collected using a micro-PL setup and a laser excitation wavelength of 532 nm. Figure 2 shows a representative PL spectrum, which exhibits a main emission peak at 1.87 eV, consistently with the typical observation of a direct-bandgap transition in singlelayer MoS 2 . [2,3,23]Furthermore, the deconvolution analysis revealed the presence of three contributions to the emission spectrum, that is, the exciton peaks A 0 (at 1.87 eV) and B (at 1.98 eV) and a trionic contribution A À (at 1.79 eV), typically reported for high-crystalline-quality 1L-MoS 2 . [23]It is worth mentioning that high defects density in single-layer MoS 2 results in a significant quenching of the PL intensity, associated with nonradiative recombination processes, and in the introduction of a specific defect-related peak (X D ) in the PL spectrum. [24,25]hus, an intense PL emission and the absence of X D contribution after the deconvolution analysis provide strong evidences of the high crystal quality of the CVD MoS 2 domains on 4H-SiC.
The thickness uniformity, strain, and doping of the CVD-grown MoS 2 on 4H-SiC were further investigated by Raman mapping.Figure 3a shows a representative Raman spectrum of as-grown MoS 2 , where the characteristic peaks associated with the in-plane (E 2g ) and out-of-plane (A 1g ) MoS 2 vibrational modes are clearly identified.The two Raman peaks have been optimally fit by Lorentzian functions with a very small full width at half maximum i.e., %3.7 and 4.8 cm À1 , which confirms the high crystal quality of the MoS 2 domains.Furthermore, the deconvolution procedure revealed the presence of a very small defect-related LO(M) component at %379.9 cm À1 , [26] probably associated with the edges of the triangular domains.These results are comparable to the state-of-art MoS 2 obtained by CVD.The thickness uniformity of the MoS 2 domains was evaluated by Raman mapping from the frequency difference Δω = ω A1g -ω E2g of the two Raman modes, which is commonly correlated to MoS 2 layer number. [27]The histogram in Figure 3b shows the statistical distribution of the Δω values extracted from an array of 2500 Raman spectra.The number of MoS 2 layers corresponding to the different Δω ranges is also reported on the top horizontal scale, indicating that the film is mostly composed of 1L-MoS 2 (Δω between 18 and 21.5 cm À1 ), with a small percentage of 2L-MoS 2 (Δω between 21.5 and 23 cm À1 ).
[30] In particular, the strain (ε) and doping (n) parameters are related to the frequencies of the E 2g and A 1g peaks by the following equation where ω m (m = E 2g or A 1g ) represents the measured frequencies of the vibrational modes, ω 0 m the values for the ideal unstrained and undoped monolayer MoS 2 , the parameters γ m (Grüneisen parameters) rule peaks' shift as a function of the strain, [31,32] while k m rules the shift as a function of doping. [33]In particular, ω 0 E2g = 385 cm À1 and ω 0 A1g = 405 cm À1 literature values for a suspended MoS 2 membrane [34] have been taken as good approximations for the unstrained/undoped MoS 2 case.
Equation ( 1) can be graphically solved by the correlative plot in Figure 3c, where the red and black continuous lines represent the theoretical strain and doping lines, respectively, and their intersection (grey square) is the ðω 0 E2g , ω 0 A1g Þ value for suspended 1L-MoS 2 .The two red arrows along the strain line indicate the direction for the tensile and compressive strain, while the yellow and white areas in the ω A1g versus ω E2g diagram indicate the n-type and p-type doping regions respectively.Furthermore, the black and red dashed lines serve as guides for the eye to estimate the ε and n values, with the separation between dashed red and black lines corresponding to step of AE 0.1% and AE 0.2 Â 10 13 cm À2 for the strain and doping, respectively.The black points in Figure 3c represent the experimental peak frequencies deduced from the 2500 Raman spectra measured on the 1L-MoS 2 /4H-SiC.The cloud of points falls in the white area of the plot, corresponding to the p-type doping region.Furthermore, they are nearly equally distributed around the doping line, corresponding to quasiunstrained MoS 2 .Figure 3d,e shows the histograms of the biaxial strain and doping values evaluated from the correlative plot.The strain distribution (Figure 3d) exhibits a peak at ε = 0.03% and a standard deviation of 0.09%.These very low strain values are consistent with the low in-plane lattice mismatch between MoS 2 and 4H-SiC.Furthermore, from doping distribution in Figure 3d, an average p-type doping of 0.45 Â 10 13 cm À2 with a standard deviation of 0.11 Â 10 13 cm À2 was evaluated for the CVD-grown 1L-MoS 2 on 4H-SiC.
MoS 2 doping can be due either to charge transfer phenomena with the substrate or overlayers or to the presence of native defects or impurities in the 2D crystal active as donor/acceptor levels.[40] p-type behavior due to electron transfer to the substrate has been reported in the case of MoS 2 monolayers exfoliated on the surface of gold films. [29,41]On the other hand, substitutional p-type doping of MoS 2 has been obtained by introducing cation species (such as Nb, [42] Zn, [43] and Ta [44] ) during growth.Alternatively, the incorporation of MoO 3 in the MoS 2 lattice results in p-type behavior, ascribed to the high work function of MoO 3 which causes a Fermi-level shift toward the valence band.This has been achieved by oxygen plasma post-treatments of exfoliated or CVDgrown MoS 2 , [45,46] associated with unintentionally incorporated oxygen during MoS 2 deposition [47] or the presence of MoO 3 residuals in MoS 2 layers produced by sulfurization of predeposited MoO x films. [18,25,48]In particular, we recently demonstrated the formation of a highly p-type-doped 1L MoS 2 on 4H-SiC by the sulfurization approach, in the presence of MoO 3 detected by XPS analyses [18] Interestingly, no MoO 3 contributions were detected by XPS analyses on the CVD-grown MoS 2 sample.Hence, we expect that the p-type doping of MoS 2 on 4H-SiC deduced by Raman measurements can be related to charge transfer phenomena at the interface between these materials.To get a deeper understanding of the interface structure and electronic properties of the MoS 2 /4H-SiC heterojunction, ab initio DFT calculations have been carried out considering different configurations of the system, starting from an ideal 1L-MoS 2 /4H-SiC(0001) interface and subsequently considering the more realistic case of the SiC(0001) surface passivation by oxygen atoms.
[51] In this respect, Figure 4a shows the structural and electronic properties of the ideal, nonreconstructed 4H-SiC(0001) surface.The projected density of states calculated for wavevectors sampled along the close Γ-M-K-Γ Brillouin zone path (Figure 4a, lower panel) shows a half-filled quasiflat band within the SiC band gap, originating from the electronic contributions of mainly 3p orbitals of unsaturated Si dangling bonds.This band defines the Fermi level of the system and gives rise to mild n-type doping, due to its proximity with the conduction band of SiC.The simplest model of a MoS 2 /4H-SiC(0001) heterostructure can be constructed through the direct interaction of this ideal surface with a single-layer MoS 2 sheet, resulting in minimum energy arrangement where sulfur atoms of the MoS 2 layer relax on top of the Si surface atoms, in agreement with previous calculations. [20]Figure 4b shows the geometry of the relaxed interface, with a calculated Si─S interface bond distance of 2.24 Å and an interface binding energy of 0.73 eV atom À1 .Both characteristics indicate a strong (covalent) MoS 2 -SiC interaction, which is not consistent with the experimental evidence of a vdW gap at the MoS 2 /4H-SiC(0001) interface (see Figure 1c).Electronically, such covalent interaction between the surface atoms totally passivates the surface Si dangling bonds and removes the respective states from the bandgap region.Furthermore, the system is characterized by an extremely high level of n-type doping.DFT calculations performed on a free-standing monolayer MoS 2 (Figure S2, Supporting information) show that the latter should ideally be undoped.Hence, this n-type doping is a result of a strong hybridization between MoS 2 conduction band states with Si states originating from Si surface atoms, as illustrated in Figure S3, Supporting Information.This interaction shifts the Fermi level of the system to the (half-filled) conduction band of MoS 2 .Overall, notwithstanding the covalent interface interaction, the MoS 2 bands are still clearly visible in the band structure of the system (Figure S3, Supporting Information), having though an indirect bandgap.We note here that this high level of n-type doping is independent of the number of MoS 2 layers that are present in the structure.
This ideal model of the MoS 2 /4H-SiC(0001) system shows significant differences with respect to the experimental data, both regarding the type of interface bonding (covalent vs the experimentally deduced vdW interaction) and the doping of the MoS 2 layer (n-type vs the experimentally observed p-type doping).Such mismatch indicates that the structural/electronic characteristics of the MoS 2 /4H-SiC(0001) heterojunction may require a level of modeling that takes into account an increased interface complexity or chemical variability.
In this respect, due to the presence of oxygen gas residues in the reactor chamber, a more realistic scenario can consider the occurrence of surface oxidation of the SiC substrate during the MoS 2 CVD growth process at 700 °C. [52]Starting from the previously discussed paradigm, one monolayer (1 ML) of oxygen can be directly introduced at the MoS 2 /4H-SiC(0001) interface by inserting a single oxygen atom at the (1 Â 1) interface model (resulting in a one-to-one ratio between O and Si surface atoms).This oxygen-passivated interface shows a totally different behavior with respect to the previously considered ideal case: 1) a van der Waals interface is now formed with a calculated minimum Si-S interface distance of 3.84 Å (see Figure 5a).Electronically, the system is now strongly p-doped (Figure 5b and S4, Supporting Information).The mechanism of p-type doping is explained by the presence of a high concentration of O atoms on the surface, which induces a rehybridization of C surface atoms below the Si-terminated surface from sp 3 to sp 2 .This C rehybridization reduces the number of covalent bonds between surface Si and C atoms and, consequently, increases the number of available bonds that Si surface atoms can form with oxygen (Figure 5a).Structurally, O atoms acquire a "bridge" configuration between two surface Si atoms.The presence of sp 2 -hybridized carbon at this interface has an important impact on the electronic properties of the system, as it introduces a half-filled C 2p band within the MoS 2 bandgap, which determines the Fermi level of the entire system (Figure 5c).It is important to note here that this doping mechanism is not directly related to the electronic contributions of the oxygen atoms at the 4H-SiC(0001)/MoS 2 interface, but to the structural modifications that these introduce on the 4H-SiC surface.
Besides the previously discussed models, where oxygen passivation of the 4H-SiC(0001) surface is either absent or present at a very high coverage, intermediate situations are likely to occur due to the noncontrollable nature of oxidation in 4H-SiC surfaces.In this respect, Figure 6 shows the surface geometry and band structure of the 4H-SiC(0001)/MoS 2 heterostructure in the presence of ¼ ML and ½ ML of atomic oxygen coverage.We note that for these calculations, a 2 Â 2 interface model has been considered.In both cases, the binding between the two parts of the heterostructure is weak, resulting in a van der Waals interaction.Contrary to the 1 ML coverage, the substrate maintains the sp 3 bond symmetry for all atoms and no C rehybridization phenomena are observed.In the ¼ ML case, the Fermi level stands in the middle of two intragap bands that originate from nonpassivated Si surface atoms with different structural arrangements due to the proximity of nearby oxygen.As these bands are closer to the conduction band of SiC, n-type doping is expected.On the contrary, a ½ ML atomic oxygen coverage leads to a full passivation of surface Si dangling bonds, as O atoms form "bridge" configurations between two surface Si atoms.As a result, the interface does not control the Fermi level of the system.The latter may therefore be defined by other charge trapping or band shifting mechanisms, like the presence of defects (e.g., sulfur vacancies [53,54] or oxygen adatoms) [45] on the MoS 2 layer.
Finally, Table 1 summarizes the results of the ab initio calculations for the ideal and oxidized 4H-SiC(0001)/MoS 2 heterostructure, depicting a rather complex scenario with respect to the doping of the MoS 2 sheet.Only in totally nonoxidized surface areas, a covalent interaction between the SiC substrate and MoS 2 is expected, whereas surface oxidation (even partial) should lead to van der Waals interfaces.The doping level should strongly depend on the oxygen surface coverage, ranging from highly n-doped for low coverages to highly p-doped for high oxygen surface coverages.This last aspect is important, as it implies that the p-type doping of the MoS 2 sheet, which is highly desirable for the realization of microelectronic devices, can be obtained not only by defect-creating processes like the plasma oxidation treatment of the MoS 2 layer, [45] but also through proper engineering of the supporting substrate.

Conclusion
In conclusion, we combined experimental characterizations and DFT calculations to describe 1L-MoS 2 /4H-SiC heterostructures obtained by CVD.The triangular MoS 2 flakes exhibit rotational alignment with the (0001) basal plane and are subjected to a very small tensile strain (<0.1%), consistently with the very small lattice mismatch between the two crystals (<2.9%).Furthermore, p-type doping of (0.45 AE 0.11) Â 10 13 cm À2 was deduced by Raman measurements.DFT calculations of equilibrium structure and electronic bands for the MoS 2 /4H-SiC(0001) system were also performed, considering different levels of refinement of the model.A covalent bond, with a low-equilibrium Si-S distance d Si-S = 2.24 Å between the two materials and n-type doping of the MoS 2 was predicted considering the simplest model without passivation of the 4H-SiC surface.In contrast, a more realistic description of the 2D/3D heterostructures was achieved   considering passivation of the Si-terminated 4H-SiC surface by oxygen atoms.The presence of oxygen leads to vdW interaction between the MoS 2 and 4H-SiC (higher Si-S distance) and a tunable MoS 2 doping from n-to p-type moving from partial oxygen coverage (¼ ML and ½ ML) to full passivation (1 ML) of the SiC surface by oxygen atoms.The p-type doping of MoS 2 on the fully O-passivated surface was found to be caused by rehybridization of the C atoms below the Si surface from sp 3 to sp 2 .The results of these experimental and theoretical investigations provide a roadmap on the tunability of electronic properties in MoS 2 /4H-SiC heterostructures by tailoring the interface structure.

Experimental Section
MoS 2 Growth and Characterizations: MoS 2 was grown by CVD in a two-heating zones furnace.The first zone held a crucible for the sulfur powder at 150 °C, while the second one held both a crucible for the molybdenum trioxide powder and for the 4H-SiC (0001) substrate at 700 °C.The process was carried out at base pressure for 1 h maintaining a continuous Ar gas flux of 100 sccm, to transport the evaporated sulfur from the first to the second zone.
Scanning electron microscopy images were acquired by ThermoFisher Scios 2 dual-beam microscope.
Furthermore, STEM analyses of the cross-sectioned MoS 2 /SiC samples (lamella preparation with focused ion beam) were carried out with an aberration-corrected Thermofisher Themis 200 microscope.
Raman maps were carried out by a WiTec Alpha equipment, using a laser excitation at 532 nm, 1.5 mW power, and 100 Â objective.Micro-Raman and micro-PL spectra were performed by a Horiba HR-Evolution micro-Raman system with a confocal microscope (100 Â objective) and a laser excitation wavelength of 532 nm.Specifically, grating of 1800 lines mm À1 was used to acquire Raman spectra in a range from 150 to 650 cm À1 , while grating of 600 lines/mm was employed for the PL spectra.All the measurements were performed using a neutral density filter at 1% to avoid the MoS 2 degradation.
DFT Calculations: In order to study the structural and electronic properties of the 4H-SiC(0001)/MoS 2 interface in the presence of interfacial oxidation, we performed DFT calculations using the Quantum Espresso software suite. [52]In view of the experimental evidence of a van der Waals heterostructure for this system, we used the van der Waals exchange-correlation functional of Hamada, [55] which allowed for an accurate description of weakly chemisorbed bulk systems, [56] along with standard solid-state pseudopotentials [57,58] based on the Perdew-Burke-Ernzerhof functional [59] for the description of core electrons.The 4H-SiC substrate was modelled by a slab containing 16 bilayers of Si-C, whose bottom termination was passivated with hydrogen, whereas the top termination interacted with the MoS 2 layer.Considering the small mismatch between the lattice constants of MoS 2 and the surface lattice parameters of 4H-SiC(0001), a (1 Â 1) model was constructed along the interface plane, consisting of a periodically replicated quasicommensurate interface between a SiC(0001) unit area (with surface lattice parameters a = b = 3.116 Å) and a slightly compressed MoS 2 unit cell (with a compressive strain of 1.6%).For partially oxidized interfaces instead, a (2 Â 2) interface model was implemented, to account for the presence of different surface oxygen coverages.Convergence was achieved with a plane-wave cutoff kinetic energy of 50 Ry and an augmented charge density cutoff of 400 Ry, using (12 Â 12 Â 1) and (6 Â6 Â 1) Monkhorst-Pack grids [60] for the sampling of the Brillouin zone in the case of the (1 Â 1) and (2 Â 2) models, respectively.A vacuum space of at least 20 Å perpendicular to the 4H-SiC(0001)/MoS 2 interface was inserted in the simulation cell to avoid spurious interactions between the periodic replicas of the system toward the [0001] direction.The binding energy of the MoS 2 sheet on various pure and oxidized substrates was calculated as , where E tot was the ground state energy of the 4H-SiC(0001)/MoS 2 interface and E SiC /E MoS2 the respective energies of the separated parts of the heterostructure.

Figure 1 .
Figure 1.a) SEM image of the triangular MoS 2 flakes on the 4H-iC 4H-SiC(0001) surface and b) histogram of the MoS 2 triangles orientation.c) Crosssectional HAADF-STEM image of the MoS 2 /SiC heterostructure.

Figure 2 .
Figure2.Micro-PL spectrum of as-grown MoS 2 on 4H-SiC.The deconvolution analysis allows to identify three spectral contributions, that is, the exciton peaks A 0 (at 1.87 eV) and B (at 1.98 eV) and the trionic contribution A À (at 1.79 eV).

Figure 3 .
Figure 3. a) Raman spectrum of MoS 2 on 4H-SiC (black line), and deconvolution analysis (grey lines), showing the presence of the LO(M), E 2g , and A 1g peaks.b) Histogram of the frequency difference (Δω = ω A1g Àω E2g ) between the two Raman peaks.c) Correlative E 2g versus A 1g plot showing the experimental positions obtained for the CVD-grown 1L-MoS 2 on 4H-SiC.Histogram of the deduced strain d) and doping e) values for the 1L-MoS 2 on 4H-SiC.

Figure 4 .
Figure 4. a) Atomic configuration of the ideal Si-terminated 4H-SiC(0001) surface (upper) and total wavevector-resolved projected density of states along the Γ-M-K-Γ Brillouin zone path (lower).b) Atomic configuration of the MoS 2 /4H-SiC(0001) interface (upper) and total wavevector-resolved projected density of states along the Γ-M-K-Γ Brillouin zone path (lower).E F refers to the calculated Fermi level of the systems.

Figure 6 .
Figure 6.Band structure of the MoS 2 /4H-SiC(0001) interface in the presence of a partially oxidized SiC surface: ¼ ML (left) and ½ ML (right).E F refers to the calculated Fermi level of the two systems.

Figure 5 .
Figure 5. a) Atomic configuration of MoS 2 interface with the Si-terminated 4H-SiC surface fully passivated by oxygen atoms (1 ML surface coverage).b) Partial wavevector-resolved projected density of states along the Γ-M-K-Γ Brillouin zone path, showing the contributions of Mo 4d states.c) Partial wavevector-resolved projected density of states along the Γ-M-K-Γ Brillouin zone path, showing the contributions of C 2p states from sp 2 -hybridized carbon atoms.E F refers to the calculated Fermi level of the system.

Table 1 .
Binding energy per Si surface atom (in eV), minimum Si-S interface distance, and doping type for a 4H-SiC(0001)/MoS 2 interface with different oxygen coverages of the SiC surface.