Substrate Effect on Band Bending of MoSe2 Monolayer Near Mirror‐Twin Domain Boundaries

Band bending near mirror twin domain boundaries (MTBs) in a MoSe2 monolayer grown on different substrates, i.e., highly oriented pyrolytic graphite (HOPG), graphene‐on‐SiC, and crystalline Au(110), is investigated by low temperature scanning tunneling microscopy/spectroscopy. Upshift bending of the valence band edge near MTB is observed on both graphene and HOPG substrates, whereas a downshift bending is found on Au(110). For the former, the magnitudes of bending are different. This is explained based on the static charge model, where an accumulative charge exists at MTBs due to both the electrical dipole discontinuity across the MTB as well as charge transfer between the substrate and MoSe2 epilayer. The relevance of the static electric model is further affirmed by noting a geometric effect on the band bending, where it is asymmetric across the vertex of an MTB loop.


Substrate Effect on Band Bending of MoSe 2 Monolayer Near Mirror-Twin Domain Boundaries
Mengfei Yuan, Junqiu Zhang One common defect in ML molybdenum dichalcogenides (e.g., MoSe 2 and MoTe 2 ) is mirror twin domain boundary (MTB) that separates two oppositely oriented domains. [18][19][20][21][22] The MTB is metallic extending in one dimension (1D), whose structural and electronic properties have been well studied and documented before. [18][19][20][21][22][23][24] More recently, it was found that the MTBs also exhibited properties characteristic of Tomonaga-Luttinger liquids (TLL). [22,[25][26][27] Another phenomenon associated with MTBs is the band-bending of 1H-TMDs in its vicinity, where an upshift of the valence band edges has been observed near the MTBs or other grain boundaries. [5,28,29] As the interface between 1H-TMD and MTB represents a metal-semiconductor interface in low dimension, the phenomenon of band-bending at the TMD/MTB interface can be of interest from both fundamental and practical viewpoints.
In this study, we examine the effects of substrate and MTB geometry on band-bending of ML MoSe 2 . Indeed, the reason of band-bending near MTBs has been suggested to be due to a static charge effect, where there is a charge transfer between the TMD epilayer and substrate and so a net accumulation of charges at MTBs. [29,30] If so, by changing the substrate, one may expect different amounts of charge transfer and thus a variation of band-bending. The latter constitutes one of main objectives of this study. By employing low temperature scanning tunneling microscopy/spectroscopy (LT-STM/STS), we observe upshifts of the band-edges, particularly the valence band maximum (VBM), of MoSe 2 close to MTBs for samples grown on graphene or highly oriented pyrolytic graphite (HOPG), where the magnitude of band-bending varies. On the other hand, it is downshifted for samples grown on Au(110). Moreover, by examining the band-bending across a vertex of a triangular MTB loop, we find a noticeable difference in magnitude of the band-bending. These observations are consistent with the electrostatic model taking account the image charges as suggested previously. [30] Band-bending of the conduction band edge is however not obvious, leading to an apparent bandgap change near the MTBs. Band bending near mirror twin domain boundaries (MTBs) in a MoSe 2 monolayer grown on different substrates, i.e., highly oriented pyrolytic graphite (HOPG), graphene-on-SiC, and crystalline Au(110), is investigated by low temperature scanning tunneling microscopy/spectroscopy. Upshift bending of the valence band edge near MTB is observed on both graphene and HOPG substrates, whereas a downshift bending is found on Au(110). For the former, the magnitudes of bending are different. This is explained based on the static charge model, where an accumulative charge exists at MTBs due to both the electrical dipole discontinuity across the MTB as well as charge transfer between the substrate and MoSe 2 epilayer. The relevance of the static electric model is further affirmed by noting a geometric effect on the band bending, where it is asymmetric across the vertex of an MTB loop.

Introduction
Monolayer (ML) transition metal dichalcogenides (TMDs) represent an important family of two-dimensional (2D) materials that have attracted intensive research attentions in recent years. Unlike graphene, the hexagonal (H) phase TMDs are semiconductors offering a broad range of bandgaps by combining different transition metals (e.g., Mo, W, Ta) with different chalcogen elements (S, Se, Te). [1] Their bandgaps can be further tuned by changing layer thickness, [2][3][4][5] applying strain, [6,7] doping [8] and changing the stacking order, [9,10] etc. These features make them promising candidates for electronic and optoelectronic applications. [11][12][13][14][15][16][17] www.advelectronicmat.de respectively, revealing the morphological features of the MTBs (bright double lines) in MoSe 2 monolayers (note that the samples all have fractional coverages, so exposed substrate areas are also discernable in the images by darker contrasts). The inset in Figure 1a shows an atomic resolution image of a defectfree region of the sample, revealing the hexagonal lattice with the lattice constant of a ≈ 0.33 nm and the Moiré modulation of 3a, signifying the 1H-MoSe 2 layer. [31][32][33] The bright doublelines associated with each MTB suggests the MTB to be of the 4|4P-type, whose atomic structure is depicted in Figure 1d for an MTB triangular loop. [22,29] Note that all the samples had undergone gentle annealing as described in the "Experimental" section, which led to relatively long and isolated MTBs instead of dense networks in as-grown samples. [18,34] The brighter contrast of the MTBs reflects higher density of states (DOS) of the 1D metal than the surrounding regions of semiconducting 1H-MoSe 2 .

Band Bending Near MTB-Substrate Effect
We employ STS to follow electronic band variations of MoSe 2 monolayers in the vicinity of 4|4P-MTBs. Samples grown on different substrates are compared in Figure 2a-c, which present spatially resolved STS spectra (referred to as the STS maps) taken along a line normal to the straight segment of the MTBs. The x axis refers to the lateral distance from the MTB located at x = 0, and the associated defect states extends from ≈−0.75 nm to +0.75 nm as marked by shaded region in the maps. The vertical axis is the energy, where E = 0 refers to the Fermi level. The measured differential conductance dI/dV reflecting the DOS is encoded by the colored contrast, where the warm color with high intensity indicates high DOS and vice versa. From the figure, one readily identifies the band edges by noting abrupt changes of the DOS. For example, the horizontal dashed lines in Figure 2a-c mark the VBM far from the MTB defects. Obviously, close to MTBs, there is a notable band-bending of the VBM until it overlaps with the defect states at positions marked by the " × " symbol. Comparing Figure 2a-c, one notes clearly that on different substrates, the magnitude and direction of band-bending varies. Specifically, the VBM bends downward on Au but upward on HOPG or graphene. It bends more on graphene than on HOPG. In passing, we note the CBM has bent little, leading to an apparent bandgap variation of 1H-MoSe 2 close to MTB defect.
Let's focus on the band-bending of the VBM for now. Indeed, band bending near defects, grain boundaries or domain edges have been previously reported and ascribed to effects such as charge transfer and screening, strain etc. [28][29][30]35,36] By introducing MTBs in 1H-MoSe 2 , translational symmetry of lattices is broken, which would result in lattice strain as well as charge built-up at or close to the defect. The presence of strain knowingly modifies the bandgap of materials as well as bandedge alignment at heterojunctions. [37,38] Band-bending near charged defects and domain edges of TMD were accounted for by a simple electrostatic model. [29,30] In a previous study, Murray et al. investigated in detail the upward band-bending near 4|4E-MTB in MoS 2 but found no obvious band-bending near 4|4P-type MTBs. [29] For the former, the effect was ascribed to a charging effect of the defect, where the charge in MTB can be categorized into the polarization charge of density λ pol and that of the band carrier charge, λ band , with the total being λ MTB = λ pol + λ band . [29] For ideal cases, i.e., a long defect separating two mirror-twin domains of infinite size, but for non-ideal cases, a lower λ pol is expected. [39] For the band charge, it may be estimated from 2 band F λ π = − e k , [29] assuming an electron-like band as does for the 4|4P-MTB, where k F is the Fermi wave-vector. However, quantum-confinement due to finite lengths of the MTBs leads to quantization in energy and thus an energy gap at the Fermi level. [18] This gap is further enhanced by Coulomb blockade for the TLL system, relevant for samples grown on HOPG or graphene. [22,26] In this case, the band carrier density may be derived from the wave-vector k m of the highest occupied states: To access k m , we have recorded STS along MTBs of finite lengths, where intensity modulations reflecting quantum well states (QWS) are evident as exemplified in Figure 2d (from the same MTB as in Figure 2b). Firstly, one notes the period of modulations shortens with increasing energy, which is consistent with the electron-like dispersion relation of the 4|4P-MTB in MoSe 2 monolayer. [18,22,26] The highest occupied states (indicated by the red arrow on right) are at 74 meV below the Fermi level due to gap-opening at E F and featuring the effect of Coulomb blockade in the TLL. [22,26] To extract k m , we perform , respectively, which translates into The variation of λ band can be explained by the different extent of charge transfer between the different substrates and the epilayer. Indeed, graphene and HOPG have relatively lower work functions (4.14 eV for graphene and 4.59 eV for HOPG) [40,41] than that of MoSe 2 (4.66 eV), [42] so at equilibrium, electrons are transferred from the substrate to MoSe 2 , increasing the filling level of the MTB band. Conversely, Au(110) has a higher workfunction (5.39 eV) [43] Figure 2a). This discrepancy may, however, be readily remedied by assuming non-ideal polarization charge, i.e., 2 3 pol λ <     e a , which could be expected given that the MTBs are of finite lengths, often form triangular loops and encircle domains of finite sizes. [39] In any case, the qualitative change in magnitude and direction of band-bending as one changes the substrate from graphene, HOPG to Au is consistent with the amount of charge transfer judged by simple work-function considerations.
We have performed similar measurements on many different MTBs on the three substrates and Figure 3 summarizes the observed band-bending magnitude versus k m . Positive (negative) band-bending refers to upshift (downshift) bending in the plot. As seen, a qualitative change from downshift to upshift bending occurs at 0.29 m π ≈     k a , which coincides with the theoretical value of the Fermi wave-vector for a freestanding MTB. [29] This lends a support to the assignment that the extra charge than that of polarization, which has led to the

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band-bending in substrate-supported samples, originates from charge transfer between substrate and the epilayer as described.

Band Bending across Vertices of MTB Loops
Electrostatic charge induced band-bending near the 4|4P-MTB defect in 1H-MoSe 2 may be further elucidated by examining the geometry effect of charge distribution, e.g., across curved defects or vertices of triangular MTB loops. Indeed, due to mirror symmetry, band-bending at the two sides of a straight MTB line is expectedly the same as has also been seen in experiments (cf. Figure 2a-c). On the other hand, when comparing results obtained at the two sides of a curved defect, e.g., at the vertex of a triangular MTB loop, the electrostatic environment is different and so the band-bending is expectedly asymmetrical. Figure 4a shows an STM image of a 4|4P-MTB loop in MoSe 2 ML grown on graphene, whose atomic configuration is shown in Figure 1d. Such an atomic structure of the vertices of the MTB loop is consistent with a previous proposal [44,45] as well as with our scanning transmission electron microscopy (STEM) observation (refer to Figure S3, Supporting Information). Figure 4b presents the spatially resolved STS map across a vertex as indicated by the dashed arrow in Figure 4a. As in Figure 2a-c, the shaded central region in Figure 4b marks the spatial extent in which the in-gap defect states are present. Outside this region, VBM of MoSe 2 ML is seen to bend upward but with different magnitudes and extends over different distances. At the exterior side, the VBM bends as much as ≈0.47 eV whereas in the interior of the triangle, it bends by ≈0.19 eV. They are accompanied by different distance ranges of the bending, ≈2.9 nm at the exterior but ≈4.5 nm in the interior. To analyze this based on the same electrostatic model, we show in Figure 4c a schematic drawing where an MTB vertex is represented by two uniformly charged lines intersecting at 60°. Each line is assumed to be in the middle of the MoSe 2 ML, i.e., in the plane of Mo layer, and the MoSe 2 ML itself is sandwiched between graphene substrate and vacuum. Following ref. [30], screening of the line charges by both MoSe 2 and graphene is taken into account by the image charges both in vacuum and in substrate up to the nth order, so the potential profile of MoSe 2 as function of x may be described as (refer to Supporting Information) is the potential when considering the screening effect of TMD layer only with dielectric constant ε TMD . In the expression, L is the length of the defect,  Figure 3), D = 0.67 nm (MoSe 2 monolayer thickness, 0.32 nm, plus the vdW gap between MoSe 2 and graphene, 0.35 nm), [31,46] d = 0.16 nm, L = 15 nm, ε TMD = 3.8, [47] and setting C = − 1.19 eV, the above formula results in a potential profile as shown in Figure 4d, where regions I and

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II represent respectively the exterior and interior of the vertex, and region III corresponds to the shaded region in Figure 4b over which the MTB in-gap states extend. Changing L from 5 to 50 nm, almost identical result is obtained (see Figure S2, Supporting Information), so the length of the defect is not a critical factor in determining the profile in the range. From Figure 4d, one clearly sees that at the vertex, the magnitude as well as the distance range over which the electric potential varies are asymmetrical, in qualitative agreement with the experimental findings (cf. Figure 4b). So, it lends a support to the electrostatic model for the observed band-bending. As the model could still be over-simplified, for example, charges along the defect may not be uniformly distributed close to the vertex and a perfect screening by graphene is also questionable, [30] no attempt is thus made for more quantitative comparisons between the calculated and the experimental profiles.
Finally, we wish to comment on the band gap change close to the MTBs as resulted from the less bending of the CBM. Similar phenomena have been observed before and were attributed to a strain effect. [5,28] While a tensile strain field in the vicinity of the 4|4P-type MTB has been shown to exist, it is also found more local than what is indicated by the results of Figure 2 (2-3 nm) and thus may not account for the observed results experimentally. More importantly, a tensile strain would lead to band gap narrowing, qualitatively in agreement with the findings on HOPG and graphene substrate (see Figure 2a,b), it is obviously in odd with the result on Au (Figure 2c), so such an "intrinsic" lattice strain as induced by the insertion of an MTB in a pristine MoSe 2 monolayer cannot be the sole reason for the observed bandgap change in this experiment. Strain may also develop due to lattice misfit between the TMD monolayer and substrate, but this cannot be significant given the weak van der Waals interaction between the two. Even if it existed, one expects the strain to be the same on graphene and on HOPG and thus the same bandgap variation. The fact that they are different experimentally (cf. Figure 2a,b) implies lattice misfit strain cannot be very important. An alternative source of strain may however be induced by the electric field due to the charges in MTBs. Indeed, it has been shown that monolayer TMDs exhibit in-plane piezoelectricity, [48] so the electric field will cause lattice strain near the MTBs. Specifically, as noted earlier, the MTBs on HOPG and graphene are negatively charged, whereas it is positively charged on Au. So, the electric fields will correspondingly point in opposite directions-toward or away from the MTBs respectively. The piezoelectric strain will then be tensile on HOPG and graphene, but compressive on Au. [48] Consequently, the bandgap is narrowed for the former but widened for the latter cases, [49,50] in qualitative agreement with the finding of Figure 2a-c. Very recently, bandgap renormalization by the TLL has been suggested, www.advelectronicmat.de which explicates the bandgap narrowing at MTBs. [51] However, on Au the gap has widened.

Conclusion
To conclude, we have examined the band bending of MoSe 2 near 4|4P-MTB defect on different substrates, including HOPG, graphene and crystalline Au(110). On HOPG and graphene, upshift band-bending of the VBM is observed, while on Au, downshift bending of the VBM is recorded. By measuring the wavevector of the highest occupied states of MTB band, we find the free carrier charge density in graphene-supported MTB is the highest, followed by HOPG and Au-supported samples. They correspond to different extents of charge transfer between the substrate and the epilayer. Adding the polarization charge, the estimated net charge density on MTB would predict band bending characteristics that appears consistent with the experiments. Such a substrate effect on band-bending thus points to an important factor of charge transfer between substrate and the epilayer. We further examined band-bending near the vertices of MTB loops and revealed a geometric effect, which lend support of the electrostatic model of the band-bending. However, we note much less obvious bending of the conduction band, giving rise to an apparent bandgap variation near the MTB defects. The reason behind remains elusive, and we argue that strain caused by the piezoelectric effect due to charges at the MTBs could be a relevant factor.

Experimental Section
Sample Preparation: ML MoSe 2 samples were grown by molecular beam epitaxy (MBE) from elemental sources, i.e., Mo metal from an e-beam cell operated at ≈50 W and Se from a conventional Knudsen cell at ≈125 °C. The MBE chamber had a base pressure of ≈5 × 10 −10 Torr. The growth temperature was ≈400 °C and the growth rate was ≈0.5 MLs h −1 . The latter was limited by Mo flux (≈1.5 × 10 11 atoms cm −2 s −1 ) and the flux of Se was in excess at ≈1.2 × 10 12 molecules cm −2 s −1 according to beam-equivalent pressure estimation. Bilayer graphene, which served as one of the substrates for MoSe 2 deposition, was obtained by flashing SiC(001) wafer up to ≈1000 ○ C repeatedly in ultrahigh vacuum (UHV) of background pressure of ≈1 × 10 −10 Torr. The HOPG substrate was cleaved and thoroughly annealed in UHV at ≈700 °C before MoSe 2 deposition was commenced. Bulk crystalline Au(110) was cleaned by Ar + bombardment (1.5 keV, 3 × 10 −6 Torr) followed by annealing at ≈800 °C. During MoSe 2 deposition, the sample surfaces were monitored in realtime by reflection high-energy electron diffraction (RHEED) operated at 15 keV. After the MBE growth, the samples were cooled to roomtemperature (RT) naturally before being capped by amorphous Se layers and then taken out of vacuum and transferred to a standalone Unisoku 1500 STM system for STM/S experiments. For samples grown on graphene and HOPG, they were annealed at ≈700 °C for 40 min to desorb the Se capping layer as well as to lower the MTB density in sample. [34] For samples grown on Au(110) substrate, the annealing temperature was ≈500 °C.
STM/S Characterization: STM/S experiments were carried out in a Unisoku 1500 STM system at 5 and 77 K, which had a base pressure of ≈2 × 10 −10 Torr. The constant current mode was adopted throughout, where the tunneling current was set at 100 pA unless stated explicitly the otherwise. Differential conductance (dI/dV) spectra were acquired by the lock-in technique with a modulation voltage of 15 mV and frequency of 1.009 kHz. The STM tip was prepared by electrochemical etching of a tungsten wire in 1.6 mol L −1 NaOH solution, and calibrated on crystalline Ag(111) surface before scan.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.