The Contact Properties of Monolayer and Multilayer MoS2-Metal van der Waals Interfaces

The contact resistance formed between MoS2 and metal electrodes plays a key role in MoS2-based electronic devices. The Schottky barrier height (SBH) is a crucial parameter for determining the contact resistance. However, the SBH is difficult to modulate because of the strong Fermi-level pinning (FLP) at MoS2-metal interfaces. Here, we investigate the FLP effect and the contact types of monolayer and multilayer MoS2-metal van der Waals (vdW) interfaces using density functional theory (DFT) calculations based on Perdew–Burke–Ernzerhof (PBE) level. It has been demonstrated that, compared with monolayer MoS2-metal close interfaces, the FLP effect can be significantly reduced in monolayer MoS2-metal vdW interfaces. Furthermore, as the layer number of MoS2 increases from 1L to 4L, the FLP effect is first weakened and then increased, which can be attributed to the charge redistribution at the MoS2-metal and MoS2-MoS2 interfaces. In addition, the p-type Schottky contact can be achieved in 1L–4L MoS2-Pt, 3L MoS2-Au, and 2L–3L MoS2-Pd vdW interfaces, which is useful for realizing complementary metal oxide semiconductor (CMOS) logic circuits. These findings indicated that the FLP and contact types can be effectively modulated at MoS2-metal vdW interfaces by selecting the layer number of MoS2.

The Schottky barrier height (SBH) serves as a crucial parameter for contact resistance in a metal-semiconductor contact, which essentially determines the efficiency of charge transport and has a significant influence on device performance [16].According to the Schottky-Mott rule, we can modulate the SBH by using metal electrodes with different work functions and obtain low contact resistance.However, the SBH actually exhibits a weak dependency on metal work functions due to the strong Fermi-level pinning (FLP) effect [17][18][19].The pinning factor S, ranging from 0 to 1, is an indicator used for evaluating the strength of FLP effect.S = 1 suggests no pinning at the metal-semiconductor interface, whereas S approaching 0 implies that the FLP is getting stronger.For instance, although metals with high work functions (such as Au and Pd) are used as electrodes, the MoS 2based field effect transistors (FETs) always exhibit n-type Schottky contacts due to the strong FLP effect [20].Therefore, reducing the FLP effect is significantly important for achieving the tunable SBH and thus creating high-performance electrical devices.
Commonly, the strong interactions at the metal-semiconductor interfaces lead to the localized density of states, which will induce the FLP effect.Metal-induced gap states (MIGS) [21] and defect/disorder-induced gap states (DIGS) [22] are important factors for contributing to the FLP effect.The DIGS can be neglected at the high-quality metal-semiconductor interfaces.Additionally, the interface dipole is another factor that contributes to the FLP effect, which is induced by the redistribution of charge at the metalsemiconductor interfaces [23,24].Thus, reducing the MIGS and the interface dipole is important for weakening the FLP effect.
Up to date, many strategies have been adopted to reduce the FLP effect, such as utilizing edge contact [25,26], inserting buffer layers [27,28], and using 2D metals as electrodes [11,13,14,29,30].Adopting the edge-contact strategy, Yang et al. [26] successfully weakened the FLP effect between Pd and MoS 2 , thereby achieving an S value of 0.975, obeying the Schottky-Mott rule.The transition metal oxides (TMOs) have been used as insertion materials for reducing the FLP effect [28].A reduced FLP effect and tunable SBH can be achieved in CrX 3 (X = I, Br)/2D metal contacts [29].However, the edge-etching process is complicated, and inserting buffer layers is often hindered by the deposition conditions [31].
Compared to the above-mentioned strategies, the van der Waals (vdW) contact between 2D semiconductors and bulk metals presents superiority for reducing the FLP effect because the vdW contact will create the ultraclean surface without damaging the structure of 2D materials [32][33][34][35][36]. Compared with traditional metal-deposition techniques [37,38] used for constructing close interfaces, the low-energy vdW integration process physically laminates the prefabricated metal electrodes onto the MoS 2 , resulting in atomically clean vdW interfaces [33,34].Kong et al. [32] demonstrated that the vdW integration process does not impose strains or doping effects on the 2D semiconductor.Duan et al. [33] indicated that vdW integration enables efficient electron tunneling in 2D MoS 2 , demonstrating its potential for fabricating superlattices or artificial heterostructures.Liu et al. [34] reported that the use of a low-energy vdW metal-integration technique enables the creation of a MoS 2 vertical FET with an on/off ratio of 10 3 , which is related to the high-quality metalsemiconductor interface.Wang et al. [36] reported the realization of vdW contacts between In-Au alloys and monolayer MoS 2 , which achieved low-resistance contacts with excellent performance.Liu et al. [39] achieved the vdW contacts between MoS 2 and 3D metals using a transfer-metal method, and they obtained an FLP factor of S = 0.96, which is very close to the Schottky-Mott limit.Although the FLP factor close to the Schottky-Mott limit has been found in MoS 2 -metal vdW interfaces, the mechanism underlying the FLP effect is incompletely known.
On the other hand, the band structure of MoS 2 is dependent on the layer number and thus influences the contact properties [40][41][42][43][44].For example, Kou et al. [42] showed that the electronic band structure of TMDC heterostructures have a sensitive dependence on their relative thickness.Cui et al. [43] illustrated that the carrier mobility of MoS 2 -based devices can be improved by increasing the layer number of MoS 2 .Lee et al. [44] demonstrated that an extremely low SBH of 70 meV can be achieved at the Al-MoS 2 interface using trilayer MoS 2 .Therefore, the thickness of MoS 2 is also a crucial parameter for influencing the SBH and the contact resistance.
In this work, based on the density functional theory (DFT), we investigate the FLP effect and the contact types of monolayer and multilayer MoS 2 -metal vdW interfaces.Compared to monolayer MoS 2 -metal close interfaces, the FLP effect is obviously reduced in monolayer MoS 2 -metal vdW interfaces, which can be attributed to the weak MIGS and small interface dipoles at vdW interfaces.Furthermore, we found that the FLP effect in multilayer MoS 2 -metal vdW interfaces is dependent on the layer number of MoS 2 .Due to the weak FLP, the p-type Schottky contact can be achieved for high-work-function metals such as 1L-4L MoS 2 -Pt, 3L MoS 2 -Au, and 2L-3L MoS 2 -Pd vdW interfaces.These findings provide an effective method for reducing the FLP effect and thus facilitating the development of high-performance MoS 2 -based devices.

Computational Methods
The DFT calculations are carried out using the Vienna Ab initio Simulation Package (VASP) [45,46].The projector-augmented wave (PAW) [47] potentials are used to treat the electron-ion interaction.To describe the exchange-correlation interaction, the Perdew-Burke-Ernzerhof (PBE) formulation of the generalized gradient approximation (GGA) [48] is adopted.The vdW interaction between MoS 2 and metals is treated using the DFT-D3 approach within the Grimme scheme [49].A plane-wave cutoff energy of 500 eV is used.The Brillouin-zone integration is performed using a 11 × 11 × 1 k-mesh.The energy convergence criterion is 10 −5 eV and the force convergence criterion is 0.01 eV Å −1 .A vacuum region of 18 Å in the z direction is used to eliminate the interaction between the neighboring slabs.

Model Structures
The optimized lattice parameter of monolayer (1L) MoS 2 is 3.19 Å and the bandgap of 1L MoS 2 is 1.64 eV, which is in agreement with previous studies [11,50].We construct the metal surfaces using six layers of metal atoms (Al, Ag, Cu, Au, Pd, and Pt in (111) orientation).The work functions of these metals are in the range of 4.15-5.65 eV, as listed in Table 1, in agreement with the previous results [51,52].MoS 2 -metal-close and -vdW interfaces are constructed by vertically stacking MoS 2 and metal surfaces.The lattice parameter of MoS 2 is fixed and the metal's lattice constant is strained to match that of MoS 2 .The supercell match patterns are ( It can be seen from Table 1 that the lattice mismatches between MoS 2 and metal surfaces (Al, Ag, Au, Pd, and Pt in (111)) ranged from 0.42% to 4.57%.In contrast, for MoS 2 /Cu (111) surface the lattice mismatch is 6.94%.Considering the relatively large lattice mismatch between MoS 2 and Cu (111) surface, we also examine the supercell match of (4 × 4) MoS 2 /(5 × 5) Cu, which corresponds to the small lattice mismatch (0.71%).Taking a 1L MoS 2 -Cu close interface as example, we calculate its projected band structures, as shown in Figure S1 of supporting information.It can be found that the n-SBH changes slightly from 0.18 eV to 0.21 eV for MoS 2 -Cu close interfaces.The calculated result demonstrates that, compared with the lattice mismatch of 6.94%, the small lattice mismatch (0.71%) has a negligible influence on the SBH value of the 1L MoS 2 -Cu close interface.Meanwhile, given that the high computational cost of multilayer MoS 2 , the supercell match of ( 111) is adopted in the following procedures.
After structural optimization, we obtained the most stable structures of 1L MoS 2 -metal close interfaces, as shown in Figure 1a-c The interlayer distance d is defined as the average distance between the S atoms and metal atoms closest to the interface in MoS2-metal close interfaces, as illustrated in Figure 1a.The optimized d values are in the range of 2.22-2.81Å for MoS2-metal close interfaces, as listed in Table 1.As for MoS2-metal vdW interfaces, the interlayer distances dvdW are set as d vdW = R S vdW + R metal vdW , where R S vdW and R metal vdW are the vdW radii of S atoms and metal atoms [53], respectively, as shown in Figure 1d.The calculated dvdW values are between 3.46 and 3.60 Å (listed in Table 1), which is larger than that of close interfaces, implying a weak interaction at MoS2-metal vdW interfaces.
To examine the stability of 1L MoS2-metal-close and -vdW interfaces, we calculate their binding energies.The binding energies can be defined as E b = (E MoS 2 /metal − E MoS 2 − E metal )/N, where E MoS 2 /metal , E MoS 2 and E metal are the total energies of 1L MoS2-metalclose and -vdW interfaces, MoS2, and metal surfaces, respectively.N is the number of Mo atoms in 1L MoS2-metal-close and -vdW interfaces.According to the definition, the negative binding energy demonstrates that 1L MoS2-metal-close and -vdW interfaces are energetically stable.As listed in Table 1, for 1L MoS2-metal close interfaces the binding energies vary from −0.98 eV to −0.42 eV.In contrast, for 1L MoS2-metal vdW interfaces, the binding energies range from −0.43 eV to −0.29 eV.These results indicate that 1L MoS2metal-close and -vdW interfaces are energetically favorable.In addition, we found that 1L MoS2-metal close interfaces have greater negative binding energies than those of the corresponding 1L MoS2-metal vdW interfaces, suggesting that 1L MoS2-metal close interfaces are more favorable than the equivalent vdW interfaces.The interlayer distance d is defined as the average distance between the S atoms and metal atoms closest to the interface in MoS 2 -metal close interfaces, as illustrated in Figure 1a.The optimized d values are in the range of 2.22-2.81Å for MoS 2 -metal close interfaces, as listed in Table 1.As for MoS 2 -metal vdW interfaces, the interlayer distances d vdW are set as and R vdW metal are the vdW radii of S atoms and metal atoms [53], respectively, as shown in Figure 1d.The calculated d vdW values are between 3.46 and 3.60 Å (listed in Table 1), which is larger than that of close interfaces, implying a weak interaction at MoS 2 -metal vdW interfaces.
To examine the stability of 1L MoS 2 -metal-close and -vdW interfaces, we calculate their binding energies.The binding energies can be defined as E b = (E MoS 2 /metal − E MoS 2 − E metal )/N, where E MoS 2 /metal , E MoS 2 and E metal are the total energies of 1L MoS 2 -metal-close and -vdW interfaces, MoS 2 , and metal surfaces, respectively.N is the number of Mo atoms in 1L MoS 2 -metal-close and -vdW interfaces.According to the definition, the negative binding energy demonstrates that 1L MoS 2 -metal-close and -vdW interfaces are energetically stable.As listed in Table 1, for 1L MoS 2 -metal close interfaces the binding energies vary from −0.98 eV to −0.42 eV.In contrast, for 1L MoS 2 -metal vdW interfaces, the binding energies range from −0.43 eV to −0.29 eV.These results indicate that 1L MoS 2 -metal-close and -vdW interfaces are energetically favorable.In addition, we found that 1L MoS 2 -metal close interfaces have greater negative binding energies than those of the corresponding 1L MoS 2 -metal vdW interfaces, suggesting that 1L MoS 2 -metal close interfaces are more favorable than the equivalent vdW interfaces.

SBH of 1L MoS 2 -Metal-Close and -vdW Interfaces
Based on the Schottky-Mott model [21], the n-type SBH (Φ n ) and p-type SBH (Φ p ) are defined as Φ n = E CBM − E F , Φ p = E F − E VBM , respectively.Where E CBM , E F , and E VBM are the conduction band minimum (CBM), the Fermi energy, and the valence band maximum (VBM), respectively.The n-type and p-type SBHs can be extracted from the projected band structures of MoS 2 -metal-close and -vdW interfaces, which are illustrated in the upper and lower panels of Figure 2, respectively.It can be observed that the Fermi level is closer to that of the CBM, indicating that the n-type Schottky contacts are formed in all 1L MoS 2 -metal close interfaces due to the strong FLP, which are in agreement with previous reports [54,55].For 1L MoS 2 -metal vdW interfaces, MoS 2 -Al (or Ag, Cu, Au, or Pd) still preserves the n-type Schottky contacts.Among them, MoS 2 -Al (or Ag or Cu) has a small n-SBH (0.15-0.25 eV), which ensures the low contact resistance that is observed experimentally [36].However, the n-type Schottky contact transforms into the p-type Schottky contact in MoS 2 -Pt-vdW interfaces, suggesting that the FLP is reduced in 1L MoS 2 -metal vdW interfaces.Therefore, it is easier to achieve p-type Schottky contact at the vdW interface between MoS 2 and high-work-function metals, which is useful for realizing complementary metal oxide semiconductor (CMOS) logic circuits [56].

SBH of 1L MoS2-Metal-Close and -vdW Interfaces
Based on the Schottky-Mott model [21], the n-type SBH (Фn) and p-type SBH (Фp) are defined as Фn = ECBM − EF, Фp = EF − EVBM, respectively.Where ECBM, EF, and EVBM are the conduction band minimum (CBM), the Fermi energy, and the valence band maximum (VBM), respectively.The n-type and p-type SBHs can be extracted from the projected band structures of MoS2-metal-close and -vdW interfaces, which are illustrated in the upper and lower panels of Figure 2, respectively.It can be observed that the Fermi level is closer to that of the CBM, indicating that the n-type Schottky contacts are formed in all 1L MoS2metal close interfaces due to the strong FLP, which are in agreement with previous reports [54,55].For 1L MoS2-metal vdW interfaces, MoS2-Al (or Ag, Cu, Au, or Pd) still preserves the n-type Schottky contacts.Among them, MoS2-Al (or Ag or Cu) has a small n-SBH (0.15-0.25 eV), which ensures the low contact resistance that is observed experimentally [36].However, the n-type Schottky contact transforms into the p-type Schottky contact in MoS2-Pt-vdW interfaces, suggesting that the FLP is reduced in 1L MoS2-metal vdW interfaces.Therefore, it is easier to achieve p-type Schottky contact at the vdW interface between MoS2 and high-work-function metals, which is useful for realizing complementary metal oxide semiconductor (CMOS) logic circuits [56].

FLP Strength of 1L MoS 2 -Metal-Close and -vdW Interfaces
To have a quantitative description of the FLP strength, we calculated the pinning factor S, which is defined as S = dΦ B /dW M , where Φ B represents the SBH and W M denotes the metal work function.Based on the definition, S = 0 denotes a strong FLP in MoS 2 -metalclose and -vdW interfaces, whereas S = 1 represents the ideal Schottky-Mott limit.The S values of 1L MoS 2 -metal-close and -vdW interfaces are fitted in Figure 3a,b.It can be seen from Figure 3a that the pinning factor S = 0.37 for 1L MoS 2 -metal close interfaces, indicating a strong FLP effect at the interface, which is in agreement with previous results [17].The pinning factor S of 1L MoS 2 -metal vdW interfaces is 0.49, which is much larger than that of the 1L MoS 2 -metal close interfaces, suggesting a weak FLP at the vdW interfaces.

SBH of Multilayer MoS2-Metal vdW Interfaces
In the following, we further consider the SBH of multilayer (2L, 3L, and 4L) MoS2metal vdW interfaces, and their projected band structures are illustrated in Figure 4. Similar to the case of the 1L MoS2-Pt vdW interface, the multilayer MoS2-Pt vdW interfaces all present p-type Schottky contacts.As the layer number of MoS2 increases, the Fermi level gradually moves close to the VBM of MoS2, leading to the decrease of the p-type SBH.Importantly, it can be seen from Figure 4c that a low p-SBH of 0.11 eV can be achieved in the 4L MoS2-Pt vdW interface, suggesting the presence of low contact resistance in MoS2based electrical devices.
For monolayer and multilayer MoS2-Al (Ag, Cu) vdW interfaces, it can be found from Figures 2g-i and 4 that the Fermi level is closer to the CBM, suggesting the formation of n-type Schottky contacts.In contrast, for MoS2-Au (Pd) vdW interfaces we found that their contact types are dependent on the layer number of MoS2.Specifically, 1L and 2L MoS2-Au vdW interfaces possess the n-type Schottky contacts, and in 3L MoS2-Au vdW interface these are changed to the p-type Schottky contact, whereas 4L MoS2-Au vdW interface transforms to the n-type Schottky contacts.Similar to the case of the MoS2-Au vdW interface, the 1L MoS2-Pd vdW interface forms n-type Schottky contacts, and in 2L and 3L MoS2-Pd vdW interfaces these transform into p-type Schottky contacts, whereas in the 4L MoS2-Pd vdW interface these change back to the n-type Schottky contacts.The transition from n-type Schottky contact to p-type Schottky contact then back to n-type Schottky contact may be correlated with the change trend of the FLP strength in monolayer and multilayer MoS2-metal vdW interfaces.The FLP strength can also be influenced by the interface dipole at MoS 2 -metal interfaces.Interface dipole formation is related to charge redistribution, which can be characterized from the charge density difference (∆ρ) at MoS 2 -metal interfaces.The charge density difference is defined as ∆ρ = ρ MoS 2 /metal − ρ MoS 2 − ρ metal , where ρ MoS 2 /metal , ρ MoS 2 , and ρ metal are the charge densities of MoS 2 -metal interfaces, the MoS 2 , and the isolated metal, respectively.To quantitatively describe the charge redistribution in 1L MoS 2 -Au close and vdW interfaces, the plane-averaged electron-density difference ∆ρ (z) along the z direction is plotted, as shown in Figures 3e and 3f, respectively.We found charge accumulation and depletion at the 1L MoS 2 -Au close and vdW interfaces, which indicate the formation of the interface dipoles.It can be seen that, compared with the case of the 1L MoS 2 -Au close interface (Figure 3e), the charge redistribution of the 1L MoS 2 -Au vdW interface (Figure 3f) is obviously reduced.This implies that the interface dipole at the 1L MoS 2 -Au vdW interface is much smaller than that of 1L MoS 2 -Au close interface.We also plot the plane-averaged electron density difference ∆ρ (z) of 1L MoS 2 -Al (Ag, Cu, Pd and Pt) close and vdW interfaces, as displayed in Figure S3 in the supporting information.The same change trend is found for the other metal electrodes in 1L MoS 2 -metal-close and -vdW interfaces.Moreover, it can be found from Table S1 of the supporting information that the amount of charge transfer for 1L MoS 2 -metal vdW interfaces is lower than that for 1L MoS 2 -metal close interfaces, which is consistent with the analysis in Figure 3e,f.Therefore, as compared with the FLP of 1L MoS 2 -metal close interfaces, the reduced FLP strength in 1L MoS 2 -metal vdW interfaces can be attributed to its relatively few MIGS and small interface dipole.

SBH of Multilayer MoS 2 -Metal vdW Interfaces
In the following, we further consider the SBH of multilayer (2L, 3L, and 4L) MoS 2metal vdW interfaces, and their projected band structures are illustrated in

FLP Strength of Multilayer MoS2-Metal vdW Interfaces
To understand the FLP strength of multilayer MoS2-metal vdW interfaces, according to their SBHs, we plot the pinning factors of 2L, 3L, and 4L MoS2-metal vdW interfaces, as shown in Figures 5b, 5c and 5d, respectively.For comparison, the pinning factor of 1L MoS2-metal vdW interface is also displayed in Figure 5a.It is found that the pinning factors of MoS2-metal vdW interfaces are dependent on the layer number of MoS2.Specifically, as the layer number of MoS2 increases from 1L to 3L, the pinning factor increases from 0.49 to 0.54 to 0.65, indicating that the FLP effect is gradually weakened.In contrast, for the 4L MoS2-metal vdW interface the pinning factor decreases to 0.47, suggesting increased FLP.The trend of FLP strength changing as the layer number of MoS2 changes can be used to explain the contact type transition in MoS2-Au (Pd) vdW interfaces.Taking the For monolayer and multilayer MoS 2 -Al (Ag, Cu) vdW interfaces, it can be found from Figures 2g-i

Conclusions
In summary, based on DFT calculations we investigate here the FLP effect and the contact types of monolayer and multilayer MoS2-metal vdW interfaces.It can be observed that the pinning factor of monolayer MoS2-metal vdW interfaces is obviously larger than that of the corresponding close interfaces, indicating that the FLP is weakened at monolayer MoS2-metal vdW interfaces.As the layer number of MoS2 increases from 1L to 3L, the pinning factor gradually increases, suggesting that the FLP effect is weakened for MoS2-metal vdW interfaces.Also, for 4L MoS2-metal vdW interfaces the pinning factor

Conclusions
In summary, based on DFT calculations we investigate here the FLP effect and the contact types of monolayer and multilayer MoS 2 -metal vdW interfaces.It can be observed that the pinning factor of monolayer MoS 2 -metal vdW interfaces is obviously larger than that of the corresponding close interfaces, indicating that the FLP is weakened at monolayer MoS 2 -metal vdW interfaces.As the layer number of MoS 2 increases from 1L to 3L, the pinning factor gradually increases, suggesting that the FLP effect is weakened for MoS 2metal vdW interfaces.Also, for 4L MoS 2 -metal vdW interfaces the pinning factor decreases to 0.47, suggesting an increase in FLP.The influence of MoS 2 layer-number on the FLP effect can be attributed to the charge redistribution at the MoS 2 -metal and MoS 2 -MoS 2 interfaces.In addition, the p-type Schottky contact can be achieved in 1L-4L MoS 2 -Pt, 3L MoS 2 -Au, and 2L and 3L MoS 2 -Pd vdW interfaces, which is related to the change of the FLP effect with the change in layer number of MoS 2 .The p-type Schottky contact is useful for realizing CMOS logic circuits.Our findings demonstrate that the FLP and contact types can be effectively modulated in MoS 2 -metal vdW interfaces dependent on the layer number of MoS 2 , which is helpful for reducing contact resistance and promoting the performance of MoS 2 -based devices.

13 Figure 1 .
Figure 1.The top and side views for (a) 1L MoS2-Al/Pt, (b) 1L MoS2-Ag/Cu/Au, and (c) 1L MoS2-Pd.(d) Schematic illustration of the interlayer distance (dvdW); R S vdW and R metal vdW are the vdW radii of S atoms and metal atoms, respectively.(e) The band alignments of MoS2 and metals.Ec, Ev, and ΔEg represent the conduction band edge, valence band edge.and band gap of MoS2, respectively.

Figure 1 .
Figure 1.The top and side views for (a) 1L MoS 2 -Al/Pt, (b) 1L MoS 2 -Ag/Cu/Au, and (c) 1L MoS 2 -Pd.(d) Schematic illustration of the interlayer distance (d vdW ); R vdW S and R vdW metal are the vdW radii of S atoms and metal atoms, respectively.(e) The band alignments of MoS 2 and metals.E c , E v , and ∆E g represent the conduction band edge, valence band edge.and band gap of MoS 2 , respectively.

Figure 2 .
Figure 2. The projected band structures of (a-f) 1L MoS 2 -metal close interfaces and (g-l) 1L MoS 2metal vdW interfaces.The gray curves represent the band structures of MoS 2 -metal interfaces.The red-dotted curves denote the band structures of MoS 2 .

Figure 3 .
Figure 3.The SBHs versus the metal work functions for (a) 1L MoS2-metal close and (b) 1L MoS2metal vdW interfaces.The partial density of states (PDOS) of (c) 1L MoS2-Au close and (d) 1L MoS2-Au vdW interfaces.The magnified PDOS represents the MIGS.The valence band is shaded in blue and the conduction band is shaded in orange.(e) The plane average charge-density difference Δρ (z) of 1L MoS2-Au close and (f) 1L MoS2-Au vdW interface.The red and blue colors represent charge accumulation and depletion, respectively.

Figure 3 .
Figure 3.The SBHs versus the metal work functions for (a) 1L MoS 2 -metal close and (b) 1L MoS 2metal vdW interfaces.The partial density of states (PDOS) of (c) 1L MoS 2 -Au close and (d) 1L MoS 2 -Au vdW interfaces.The magnified PDOS represents the MIGS.The valence band is shaded in blue and the conduction band is shaded in orange.(e) The plane average charge-density difference ∆ρ (z) of 1L MoS 2 -Au close and (f) 1L MoS 2 -Au vdW interface.The red and blue colors represent charge accumulation and depletion, respectively.To understand the weak FLP in 1L MoS 2 -metal vdW interfaces, taking 1L MoS 2 -Au as an example, the projected density of states (PDOS) of Mo and S atoms are calculated and displayed in Figure 3c,d.For a 1L MoS 2 -Au close interface, a large number of Mo-d and S-p states are extended to the forbidden band of MoS 2 , leading to the obvious MIGS that can be seen from the magnified PDOS inserted in Figure 3c.Compared with the case of the 1L MoS 2 -Au close interface, the MIGS are notably reduced in the 1L MoS 2 -Au vdW interface, as shown in Figure 3d.We also calculate the PDOS of 1L MoS 2 -Al (Ag, Cu, Pd and Pt) close and vdW interfaces, as shown in Figure S2 in the supporting information.We found that, similar to the case of the 1L MoS 2 -Au vdW interface, fewer MIGS are also found in 1L MoS 2 -Al (Ag, Cu, Pd and Pt) vdW interfaces.The FLP strength can also be influenced by the interface dipole at MoS 2 -metal interfaces.Interface dipole formation is related to charge redistribution, which can be characterized from the charge density difference (∆ρ) at MoS 2 -metal interfaces.The charge density difference is defined as ∆ρ = ρ MoS 2 /metal − ρ MoS 2 − ρ metal , where ρ MoS 2 /metal , ρ MoS 2 , and ρ metal are the charge densities of MoS 2 -metal interfaces, the MoS 2 , and the isolated metal, respectively.To quantitatively describe the charge redistribution in 1L MoS 2 -Au close and vdW interfaces, the plane-averaged electron-density difference ∆ρ (z) along the z direction is plotted, as shown in Figures3e and 3f, respectively.We found charge accumulation and depletion at the 1L MoS 2 -Au close and vdW interfaces, which indicate the formation of the interface dipoles.It can be seen that, compared with the case of the 1L MoS 2 -Au close interface (Figure3e), the charge redistribution of the 1L MoS 2 -Au vdW interface (Figure3f) is obviously reduced.This implies that the interface dipole at the 1L MoS 2 -Au vdW interface is much smaller than that of 1L MoS 2 -Au close interface.We also plot the plane-averaged electron density difference ∆ρ (z) of 1L MoS 2 -Al (Ag, Cu, Pd and Pt) close

Figure 4 .
Similar to the case of the 1L MoS 2 -Pt vdW interface, the multilayer MoS 2 -Pt vdW interfaces all present p-type Schottky contacts.As the layer number of MoS 2 increases, the Fermi level gradually moves close to the VBM of MoS 2 , leading to the decrease of the p-type SBH.Importantly, it can be seen from Figure 4c that a low p-SBH of 0.11 eV can be achieved in the 4L MoS 2 -Pt vdW interface, suggesting the presence of low contact resistance in MoS 2 -based electrical devices.24, 14, x FOR PEER REVIEW 8 of 13

Figure 4 .
Figure 4.The projected band structures of (a) 2L MoS2-metal vdW interfaces, (b) 3L MoS2-metal vdW interfaces, and (c) 4L MoS2-metal vdW interfaces.The gray curves represent the band structures of MoS2-metal interfaces.The red-dotted curves denote the band structures of MoS2.

Figure 4 .
Figure 4.The projected band structures of (a) 2L MoS 2 -metal vdW interfaces, (b) 3L MoS 2 -metal vdW interfaces, and (c) 4L MoS 2 -metal vdW interfaces.The gray curves represent the band structures of MoS 2 -metal interfaces.The red-dotted curves denote the band structures of MoS 2 .
and 4 that the Fermi level is closer to the CBM, suggesting the formation of n-type Schottky contacts.In contrast, for MoS 2 -Au (Pd) vdW interfaces we found that their contact types are dependent on the layer number of MoS 2 .Specifically, 1L and 2L MoS 2 -Au vdW interfaces possess the n-type Schottky contacts, and in 3L MoS 2 -Au vdW interface these are changed to the p-type Schottky contact, whereas 4L MoS 2 -Au vdW interface transforms to the n-type Schottky contacts.Similar to the case of the MoS 2 -Au vdW interface, the 1L MoS 2 -Pd vdW interface forms n-type Schottky contacts, and in 2L and 3L MoS 2 -Pd vdW interfaces these transform into p-type Schottky contacts, whereas in the 4L MoS 2 -Pd vdW interface these change back to the n-type Schottky contacts.The transition from n-type Schottky contact to p-type Schottky contact then back to n-type Schottky contact may be correlated with the change trend of the FLP strength in monolayer and multilayer MoS 2 -metal vdW interfaces.3.5.FLP Strength of Multilayer MoS 2 -Metal vdW Interfaces To understand the FLP strength of multilayer MoS 2 -metal vdW interfaces, according to their SBHs, we plot the pinning factors of 2L, 3L, and 4L MoS 2 -metal vdW interfaces, as shown in Figures 5b, 5c and 5d, respectively.For comparison, the pinning factor of 1L MoS 2 -metal vdW interface is also displayed in Figure 5a.It is found that the pinning factors of MoS 2 -metal vdW interfaces are dependent on the layer number of MoS 2 .Specifically, as layer number of MoS 2 increases from 1L to 3L, the pinning factor increases from 0.49 to 0.54 to 0.65, indicating that the FLP effect is gradually weakened.In contrast, for the 4L MoS 2 -metal vdW interface the pinning factor decreases to 0.47, suggesting increased FLP.The trend of FLP strength changing as the layer number of MoS 2 changes can be used to explain the contact type transition in MoS 2 -Au (Pd) vdW interfaces.Taking the MoS 2 -Au vdW interface as an example, as the layer number of MoS 2 increases to 3L the FLP strength is weakened, and thus the 3L MoS 2 -Au vdW interface is changed to the p-type Schottky contact due to the high work function of Au.When MoS 2 increases to 4L, the FLP strength is increased, so the 4L MoS 2 -Au vdW interface transforms back to the n-type Schottky contact.The trend of contact type changing as the layer number of MoS 2 changes is related to the change of FLP strength in the MoS 2 -Au vdW interface, which complies with Schottky-Mott rules.Nanomaterials 2024, 14, x FOR PEER REVIEW 9 of 13

Figure 5 .
Figure 5.The SBHs versus the metal work functions for (a) 1L MoS2-metal vdW interfaces, (b) 2L MoS2-metal vdW interfaces, (c) 4L MoS2-metal vdW interfaces, and (d) 4L MoS2-metal vdW interfaces.The pinning factors S are marked in the pictures.3.6.Layer-Dependent FLP Strength AnalysisNext, we analyze the influence of MoS2 layer-number on the FLP effect.Taking monolayer and multilayer MoS2-Au vdW interfaces as examples, we plotted their plane-average charge-density difference along the z-axis, as illustrated in the left panels of Figure6.The schematic illustrations of charge transfer at MoS2-Au and MoS2-MoS2 interfaces are displayed in the right panels of Figure6.It can be found from Figure6athat the charge accumulates at the Au side and depletes at the MoS2 side, indicating that the charge transfers from MoS2 to Au, thus creating an interface dipole pointing from Au to MoS2 at the 1L MoS2-Au vdW interface.For the 2L MoS2-Au vdW interface (Figure6b), the charge 1st-layer 2nd-layer

Figure 5 .
Figure 5.The SBHs versus the metal work functions for (a) 1L MoS 2 -metal vdW interfaces, (b) 2L MoS 2 -metal vdW interfaces, (c) 4L MoS 2 -metal vdW interfaces, and (d) 4L MoS 2 -metal vdW interfaces.The pinning factors S are marked in the pictures.3.6.Layer-Dependent FLP Strength Analysis Next, we analyze the influence of MoS 2 layer-number on the FLP effect.Taking monolayer and multilayer MoS 2 -Au vdW interfaces as examples, we plotted their plane-average charge-density difference along the z-axis, as illustrated in the left panels of Figure 6.

Figure 6 .
Figure 6.The plane-average charge-density difference (in the left planes) and the schematic illustration of charge transfer (in the right planes) of (a) 1L MoS2-Au vdW interface, (b) 2L MoS2-Au vdW interface, (c) 3L MoS2-Au vdW interface, and (d) 4L MoS2-Au vdW interface.The arrows represent the direction of interface dipoles.

Figure 6 .
Figure 6.The plane-average charge-density difference (in the left planes) and the schematic illustration of charge transfer (in the right planes) of (a) 1L MoS 2 -Au vdW interface, (b) 2L MoS 2 -Au vdW interface, (c) 3L MoS 2 -Au vdW interface, and (d) 4L MoS 2 -Au vdW interface.The arrows represent the direction of interface dipoles.

Table 1 .
Calculated interfacial properties of MoS 2 -metal-close and -vdW interfaces.W M (eV) is the metal work function and δ (%)