Mechanism of charge redistribution at the metal–semiconductor and semiconductor–semiconductor interfaces of metal–bilayer MoS₂ junctions Open Access

The potential applications of two-dimensional (2D) semiconducting transition-metal dichalcogenides (TMDs) in electronics^1–5 and optoelectronics^6–8 have stimulated intensive research of their fundamental properties as well as the metal–semiconductor junctions (MSJs) based on them. MoS₂, as the representative TMDs, shows strong optical absorption^9,10 and high on/off current ratio.¹¹ However, in contacting MoS₂ to metal electrodes, there is an unexpectedly high electrical contact resistance, which reduces the field-effect mobility of charge carriers across the interface of MSJ and degrades device performance.¹² The non-ohmic behavior at metal–MoS₂ interfaces indicates the existence of significant Schottky barrier height (SBH), which depends on the energy level alignment between isolated MoS₂ and metal in the ideal Schottky–Mott limit.¹³ Realistically, there is a serious deviation from the Schottky–Mott limit especially for MoS₂ contacts to 3D metal electrodes due to the strong Fermi-level pinning (FLP) caused by the interface dipole formed due to the asymmetric charge redistribution at the metal–MoS₂ interface, even for a high-quality interface without defects/disorder.¹⁴ The charge density redistribution at the metal–MoS₂ interface is collectively contributed by several factors, including (quasi-)chemical interaction, metal-induced gap states (MIGS), pushback effect that pushes electrons back to metal, and charge transfer induced by the tendency of MoS₂ band edges aligning with the metal Fermi-level.¹⁵ 

Recently, the study of metal–multilayered 2D semiconductor junctions and their thickness-dependent performance has attracted increasing attention.^16–20 Layer-number engineering of 2D semiconductors offers a new controlling factor to tune device-performance. For example, the electric current and photocurrent varying as a function of the layer-number in devices based on multilayered 2D semiconductors were reported,¹⁶ and we proposed type II band alignment in 2D multilayered semiconductor homojunctions by supporting them on metals.¹⁹ It is worth noting that layer-number engineering plays a leading role only for few-layer 2D semiconductors, especially for less than four layers.²¹ Therefore, the mechanisms of layer-number-dependence of MSJs with multilayered MoS₂, which contains the metal–MoS₂ and MoS₂–MoS₂ interfaces, deserve to be well understood.

In the current work, by first-principles density functional theory (DFT) calculations, we probe the mechanisms of asymmetric electron redistribution at metal–MoS₂ (M–S) and MoS₂–MoS₂ (S–S) interfaces in MSJ with bilayer H–MoS₂. The electron density redistribution determines both the interface dipole at M–S interfaces and the band offset between 2D semiconductor layers, which collectively determine the Schottky barrier height of metal–bilayer MoS₂ junctions. To give the dominant mechanisms for different types of MSJ, we perform a systematic study of monolayer (ML) and bilayer (BL) MoS₂ contact to 3D and 2D metals with metal work functions adjustable in a wide range. At the M–S interfaces, the pushback effect and MIGS dominate in 3D metal–MoS₂ junctions, while in 2D metal–MoS₂ junctions, significant charge transfers across the interface for MSJs with 2D metals that have extremely large or small work functions, and the “covalent-like quasi-bonding” is formed for MSJs with medium-work-function 2D metals. At the S–S interfaces, the electron density redistribution is closely related to the M–S interface (i.e., change sign or not between the two kinds of interfaces) that depends on the dimensionality (3D vs 2D) of metals, and the resulting band offset generates a type-II band alignment between MoS₂ layers¹⁹ with different mechanisms for 2D vs 3D metal contacts. General insights and new concepts are developed for MSJs with bilayer MoS₂, and the importance of semiconductor–semiconductor interlayer interaction is highlighted.

First-principles calculations were carried out using density functional theory as implemented in the Vienna ab initio Simulation Package (VASP) with periodic boundary conditions.^22–24 The projected augmented wave (PAW) method²⁵ was adopted to describe the core electrons. The valence electrons were described by plane waves with a cut-off kinetic energy of 500 eV. All the calculations were carried out using the newly developed strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) density functional²⁶ with rVV10 (the revised Vydrov–van Voorhis nonlocal correlation functional) for van der Waals (vdW) correction.²⁷ The SCAN + rVV10 method have offered a good performance for layered-materials compared with experimental results²⁸ and especially appropriate for metal–semiconductor contacts¹⁹ (see Table SI in the supplementary material for more details). The atomic positions were fully relaxed until the force on each atom was less than 0.01 eV Å⁻¹. The energy convergence value between two consecutive self-consistent steps was set as 10⁻⁴ eV. The Brillouin zone (BZ) was sampled in the Monkhorst–Pack scheme with a K-point grid spacing of 0.01 Å⁻¹. A vacuum region of 15 Å is added and a dipole correction is applied to avoid spurious interactions between periodic images of the slab.²⁹ 

The optimized lattice constant of monolayer (ML) MoS₂ is 3.16 Å, which agrees with theoretical and experimental results in the literature.^27,30,31 The geometry structures of MSJs with Mo₂C(OH)₂–MoS₂ are shown as an example in Fig. S1 and the supercells used to model the metal–MoS₂ junctions are listed in Table SII in the supplementary material. Using these supercells, the in-plane lattices mismatch between metal and MoS₂ is in the range of 2.5%–4.6%. Since the property of MoS₂ is sensitive to strain, we strain the metal lattice to adapt the MoS₂ lattice, as done in this way in the literature.^32–34 The electron affinity energy (EAE) and ionization energy (IE) of isolated ML and bilayer (BL) MoS₂ are shown in Fig. 1. The EAE is about 4.3 eV and almost unchanged from ML to BL, while the IE decreases greatly from 6.20 eV to 5.88 eV. When contacting MoS₂ with frequently used 3D metal electrodes, a sizable n-type Schottky barrier (SB) is often formed due to the strong FLP at the M–S interfaces.^32,34,35 With modulated metal work functions and dangling-bond-free surfaces, the 2D metallic MXenes contact to MoS₂ can get vanishing n-type and p-type SBH.^36,37 High-quality MXenes Mo₂CT₂ (T = O, OH, or F is the surface terminating group) acting as 2D metal electrodes have been reported both in experimental^38–40 and theoretical works.⁴¹ The work functions of 3D and 2D metals are shown in the middle panels of Fig. 1, with the geometric structures of 2D Mo₂CT₂ shown in the right. The work functions of MXenes are mainly determined by the different functional groups, which produced surface dipoles with different magnitudes and signs:⁴¹ with O-termination, it has the largest work function of 7.79 eV and with OH-termination, the smallest work function of 2.12 eV is given, whereas F-termination exhibits a medium work function of 4.81 eV, which locates within the bandgap of MoS₂ (Fig. 1). The work function of 3D metals (Ag and Pt) lies within the bandgap of monolayer MoS₂, either close to the EAE or to IE (Fig. 1).

In the MSJs with ML MoS₂, the equilibrium distances (D) between metal and MoS₂ (defined as the separation between the metal surface layer and the S atom layer of MoS₂ close to the metal) are listed in Table I, which fall in the range of typical vdW interaction for 2D metal Mo₂CF₂ and Mo₂CO₂ and stronger than typical vdW interaction for 2D metal Mo₂C(OH)₂ and 3D metal Ag and Pt (note that the differences in atomic radius of metal surface atoms should also be considered). The typical vdW interaction character (or stronger than typical vdW interaction) is further confirmed by binding energies in Table I. Here, the binding energy (E_b) between metals and MoS₂ is defined as $Eb=Etot−EM−EMoS2/A$⁠, where E_tot, E_M, and $EMoS2$ are the total energies of metal–MoS₂, isolated metal, and MoS₂, respectively, and A is the contact area in the supercell. The calculated E_b values are in the range of −0.26 J/m² to −0.37 J/m² for 2D metals Mo₂CF₂ and Mo₂CO₂, which suggests that MoS₂ is physisorbed on these 2D metals, while the E_b are −0.62 J/m² and −0.96 J/m² for Ag and Pt, which are stronger than pure vdW interactions. The stronger E_b for Mo₂C(OH)₂–ML MoS₂ (−0.82 J/m² or corresponds to −0.44 eV) is due to the synergistic effect of vdW interaction (typical vdW interstratification is −0.3 J/m² or corresponds to −0.16 eV) and hydrogen bonding (here O–H⋯S, the typical strength is −0.26 eV).^42,43 The “bond length” of hydrogen bonding O–H⋯S in Mo₂C(OH)₂–MoS₂ is 2.67 Å, which is the competition between typical hydrogen bonding (the typical bond length of O–H⋯S is about 2.33 Å⁴²) and van der Waals interaction (the sum of vdW radii of H and S is 2.95 Å).⁴³ Although the binding energies in MSJ with 3D metal or 2D metallic Mo₂C(OH)₂ are stronger than typical van der Waals interaction, they are far from chemical bonding, and all the systems we studied belong to weak interactions (or mainly physisorption).

It is noticeable here that the strong FLP at the interfaces of 3D metals (e.g., Ag and Pt) and MoS₂ becomes very weak at the interfaces of 2D metallic MXene–MoS₂. The surfaces of both 2D MoS₂ and MXene are dangling-bond-free, and hence, the weak MXene–MoS₂ interactions suppress the formation of MIGS (Figs. S3 and S4 in the supplementary material and Fig. 5 below). The vdW interaction at 2D MXene–MoS₂ interfaces makes the electron redistribution between them simple relative to that at the 3D metal–MoS₂ interfaces. For 3D metal contacts, the interaction at the M–S interface is much more complicated, and hence, multiple mechanisms work together to determine the asymmetric electron density redistribution at the interface, which will be detailed below.

In the Schottky–Mott limit, the Schottky barrier height (SBH) Φ_B is obtained by band alignment of the non-interacting subsystems (as in Fig. 1),

where $ΦBe$ and $ΦBh$ are the SBH for electrons (n-type) and holes (p-type), W_M is the work function of the metal, EAE and IE are the electron affinity and ionization energies of the semiconductor, respectively (IE − EAE = bandgap). In the Schottky–Mott limit, Φ_B linearly depends on the metal work function W_M and changes in the same amounts as W_M does. In many cases, however, even for high-quality interface without defects or disorder in weakly interacting systems, the Schottky–Mott limit may not be obeyed and the hole and electron injection barriers are different from those in Eq. (1). The origin of the differences for MSJs with 2D semiconductors can be attributed mainly to the existence of an interface dipole, ΔV,^32,33 which changes the SBHs to

The ΔV is caused by the electron density rearrangement at the M–S interface of MSJs. The electron density difference, Δρ(x, y, z), is an effective tool to analyze the bonding at metal–MoS₂ interfaces, which is defined as the difference of the electron density distribution of the composite full system and the isolated subsystems,

where ρ_tot, ρ_M, and $ρMoS2$ are the electron density of the metal–MoS₂ junction, the metal, and the free-standing MoS₂, respectively. The Δρ mainly localized around the metal–MoS₂ interface, which includes the contributions from the energy level shift induced by charge transfer, the pushback effect, and the energy level broadening induced by metal interaction, which collectively changes the SBH at the metal–semiconductor interface through interface dipole, ΔV. The ΔV (which can be also described as electrostatic potential change) satisfy the Poisson equation below as a function of Δρ.^44–46 By solving the Poisson equation, a potential step across the interface is achieved,

in which z is the distance from the middle of the M–S interface and A is the contact area. In density functional theory (DFT) calculation with a slab model, ΔV can be alternately obtained as the difference between the asymptotic values of the potential difference in the vacuum with an expression

where W_M/W_M/S are the work function of the clean metal surface/the metal surface covered by MoS₂.

The plane-averaged electron density differences along the z-direction perpendicular to the M–S interfaces, Δρ(z), are shown in Fig. 2. The metal–ML MoS₂ junctions are used for the analysis of the M–S interface of metal–bilayer MoS₂ junctions, since we find that in metal–BL MoS₂ junctions, the behavior at the M–S interface largely unchanged relative to that in metal–ML MoS₂ (also refer to Fig. 7 below).

For the 3D metal Pt–ML MoS₂ junction [Fig. 2(d)], the electron density distribution at the interface is very complicated. The pushback effect,^32,47 which is observed in the physisorption of molecules or 2D layers on metals, plays a main role at the Pt–ML MoS₂ interface. The reason for the pushback effect is the antisymmetrization of the product of the 3D metal and 2D semiconductor wave functions.⁴⁸ When 2D monolayer MoS₂ is physisorbed onto the metal surface, the two wave functions overlap (but no rehybridization as in chemical bonding). In order to reduce the Pauli repulsion at the interface overlap region, a rearrangement of the electron density occurs. Since the wave function of transition metal Pt is more extended and deformable than that of MoS₂, the electrons are pushed back into Pt, leading to the phenomenon that electrons accumulate at the Pt side and deplete at the MoS₂ side of the M–S interface. As a result, the metal work function is effectively lowered with a negative ΔV for the Pt(111) surface absorbed with MoS₂, as illustrated in Fig. 3(d) [also see Eq. (5)]. The pushback effect also occurs at the Ag–MoS₂ interface (Figs. S5 and S6), and the other factors of electron redistribution at the 3D metal–MoS₂ interface are detailed in Fig. S5 and the related text.

The charge transfer is induced by the alignment of MoS₂ band edges and 2D metal Fermi levels, which takes place at the physisorbed interface of Mo₂C(OH)₂–MoS₂ and Mo₂CO₂–MoS₂. The Fermi level of Mo₂C(OH)₂ is higher than the EAE of MoS₂, while that of Mo₂CO₂ is lower than IE of MoS₂ (Fig. 1). In the case of Mo₂C(OH)₂–MoS₂ [Fig. 2(a)], the electron is transferred from the 2D metal to MoS₂, and MoS₂ becomes negatively charged, which is further confirmed by Bader charge analysis,⁴⁹ which shows that MoS₂ obtain 0.11 electrons. The charge transfer creates a positive ΔV at the M–S interface that increases the vacuum level, as shown in Fig. 3(a). The electrons continue transfer until the conduction-band minimum (CBM) level of MoS₂ aligns close to the Fermi level of the 2D metal. Hence, an n-type vanishing SBH is obtained [Figs. 3(a) and S3(a)], and then, MoS₂ is degenerately doped [Fig. 5(a)]. In Fig. 2(b), on the contrary to Fig. 2(a), electrons transfer from MoS₂ to the 2D metal Mo₂CO₂. Bader charge analysis shows that MoS₂ lose 0.34 electrons due to the Mo₂CO₂ Fermi level that is below the IE of MoS₂. This charge transfer creates a negative ΔV at the interface and reduces the vacuum level. Therefore, a p-type vanishing SBH is obtained [Figs. 3(b) and S3(b)], and then, MoS₂ is degenerately hole doped [Fig. 5(b)].

For the Mo₂CF₂–MoS₂ interface, since the Fermi level of Mo₂CF₂ is situated in-between EAE and IE of MoS₂, there is nearly no net charge transfer across the interface and hence no interface dipole formation, and the vacuum levels of the Mo₂CF₂ and MoS₂ remain aligned [Fig. 3(c)] as that in the isolated subsystems (Fig. 1). Interestingly, we found that at the Mo₂CF₂–MoS₂ interface, electrons accumulate at the middle of the interface region and deplete at both the fluorine and the sulfur surface-layers [Fig. 2(c)]. This phenomenon between vdW 2D systems is called the formation of “covalent-like quasi-bonding,” which is similar to the literature reported electronic interlayer-hybridization in bilayer PtS₂ and in few-layered black phosphorus.⁵⁰ The electron aggregation region is a bit close to fluorine than sulfur since fluorine is more electronegative than sulfur. The polarized “covalent-like quasi-bonding” in our system occurs under the following conditions: the interaction between the two layers of different 2D materials is stronger than pure vdW interaction but much weaker than chemical interaction, and the electronegativity of the atomic layers at the left and right sides of the interface is similar to each other. The covalent-like quasi-bonding at the Mo₂CF₂–MoS₂ interface has no net charge transfer and hence will not create interface dipole. Hence, the SBH in Mo₂CF₂–MoS₂ junction follows Eq. (1) (the Schottky–Mott limit). It is interesting to note that here, we have generalized the concept of “covalent-like quasi-bonding” between the same 2D semiconductor⁵⁰ and polarized “covalent-like quasi-bonding” between two different 2D materials, and the 2D material is not limited to semiconductors but can also to metals in our case.

A comparison of the mechanisms at the M–S interfaces with 3D metal vs 2D metal: the pushback effect dominates in 3D metal–MoS₂ junctions while is not apparent in 2D metal–MoS₂ junctions, since 2D metal Mo₂CT₂ have a similar electron-accepting capability to that of 2D MoS₂, namely, the electrons spilled out of the surface are symmetrically pushed back to 2D metal and 2D MoS₂ for the 2D metal–MoS₂ junctions.

Based on all the above analyses, one can analyze the mechanism of electron density redistribution Δρ at the M–S interface and can qualitatively understand the resulted interface dipole ΔV. However, one may argue that ΔV is directly related to zΔρ(z) but not simply Δρ. Hence, in the following, we analyze zΔρ(z) and show that the conclusion simply from Δρ holds. The integration of zΔρ(z) can be derived from Eq. (4),

Figure 4 shows the zΔρ(z) plots around the M–S interfaces. In Fig. 4(a) for Mo₂C(OH)₂–MoS₂, the positive zΔρ(z) region is much more than the negative region, which gives a positive ΔV and is consistent with the analysis of Δρ(z) only in Fig. 2. For Mo₂CO₂–MoS₂, the negative zΔρ(z) region is much larger than the positive one, which gives a negative ΔV. For Mo₂CF₂–MoS₂ [Fig. 4(c)], the positive and negative regions are comparable, which give rise to a zero ΔV. In Pt(111)–MoS₂, the distribution of zΔρ(z) is complicated, and therefore, a semi-quantitative analysis from the integral of ∫zΔρ(z)dz is needed and has been carried out. The values of the integral for the junctions in Figs. 4(a)–4(d) are 0.14, −0.08, 0, and −0.05, respectively. The −0.05 for Pt(111)–MoS₂ means the formation of negative ΔV. In summary, the analysis of Δρ(z) in Figs. 2 and zΔρ(z) in Fig. 4 gives the same conclusion for ΔV.

The metal-induced gap states (MIGS)^21,33 also play a significant role in 3D metal–MoS₂ junctions in forming ΔV⁵¹ in addition to the above discussed pushback effect in 3D metal–MoS₂ junctions. The partial density of states (PDOS) of Mo₂CT₂–MoS₂ and Pt(111)–MoS₂ are displayed in Fig. 5 to explore whether the MIGS in MoS₂ can be induced by 2D and 3D metals. In Fig. 5(d) for Pt(111)–ML MoS₂, a distinct overlap between the Pt 5d, Mo 4d, and S 3p orbitals can be seen around the Fermi energy, as indicated by the arrow, suggesting orbital hybridization upon interface formation,³⁴ and MoS₂ becomes partially metallized in contacts to Pt(111). Note that in the Mo₂CF₂–MoS₂ junction [Fig. 5(c)], the MoS₂ layer remains semiconducting with a bandgap. In Figs. 5(a) and 5(b), the bandgaps exist but the Fermi level locates above the conduction band edge of MoS₂ for Mo₂C(OH)₂–MoS₂ (locates below the valence band edge of MoS₂ for Mo₂CO₂–MoS₂). Hence, MoS₂ is degenerately electron doped or degenerately hole doped in these two junctions.⁵² 

The interface dipole ΔV modifies the SBH [by Eq. (2)] and deviates from the Schottky–Mott limit [Eq. (1)]. For 2D metal contacts with very large/small work functions, the interface dipole ΔV is significant [Figs. 3(a) and 3(b)]; if the Fermi level of 2D metal is in-between EAE and IE, the ΔV is negligible [Fig. 3(c)], and the SBH can be well described by the Schottky–Mott limit [Eq. (1)]. However, for 3D metal contacts, even their work functions are located in-between EAE and IE of ML MoS₂ (such as Ag, Au, Cu, and Pt),³² and a significant ΔV appear due to the pushback effect at the 3D metal–MoS₂ interface.

The SBHs from the projected band structure (or the PDOS)^32,35,53,54 calculated by DFT, for the MoS₂–metal junctions, can be defined as

in which E_F is the Fermi level of the junction, $χMoS2$ is the EAE of MoS₂ in the MoS₂–metal junction [which is affected by the metal, but not the EAE of isolated MoS₂ as used in Eqs. (1) and (2) and in Fig. 1], and E_g is the bandgap of MoS₂ in the junction. The projected band structures of the ML MoS₂ supported on 2D metals Mo₂CT₂ and 3D metal Pt are shown in Fig. S3, and the SBHs from the DFT projected band structures are shown in Fig. 6, along with the SBH from Eqs. (1) and (2). The SBHs from DFT projected band structures are close to the ones from Eq. (2), which includes the effects of ΔV beyond the Schottky–Mott limit [Eq. (1)]. ΔV has negligible effects on SBH in the Mo₂CF₂–MoS₂ junction, since there is no MIGS and no charge transfer at its M–S interface. For all the other studied junctions, the interface dipole ΔV has a great effect on SBH, which largely makes up the difference between the result from DFT and from Eq. (1). It is worth noting that for Ag, the ΔV is small since the interaction of Ag with MoS₂ is weaker than that of Pt (Table I) due to the fully filled d bands of Ag.

Although ΔV can improve the description of SBH by Eq. (2) (close to the SBH from DFT), there is some deviation between the SBH from Eq. (2) and that from DFT, which may be resulted from other factors beyond Eq. (2), such as the magnitude of bandgap variation due to interaction with metal surface and the hydrogen bonding in Mo₂C(OH)₂–MoS₂. The bandgap of 1.88 eV from the isolated ML MoS₂ is used in Eqs. (1) and (2), while the bandgaps vary from 1.55 eV to 1.98 eV for ML MoS₂ contacting to 3D and 2D metals. Simultaneously, the work functions of metal also change under strain (see Table SIII in the supplementary material).

In the above, the various mechanisms of electron density redistribution at M–S interfaces have been discussed in metal–ML MoS₂ junctions. Comparing the electron density redistributions at the M–S interfaces in metal–BL MoS₂ junctions (Fig. 7) with that in metal–ML MoS₂ junctions (Fig. 2), one finds that the electron density redistribution is almost identical at the M–S interfaces in both junctions with ML and BL MoS₂. Then, in the following, we focus on the electron density redistributions at the S–S interfaces in Fig. 7, which give rise to band offsets between the two semiconducting layers of MoS₂ and hence may change the overall SBH in metal–BL MoS₂ junctions.

For the Mo₂C(OH)₂–BL MoS₂ and Mo₂CO₂–BL MoS₂ junctions as shown in Figs. 7(a) and 7(b), acting as a continuation of the M–S interface, the electron density redistribution at the S–S interfaces in these two junctions is the same as that in their M–S interfaces, although the magnitude decayed considerably. For Mo₂C(OH)₂–BL MoS₂ [Figs. 7(a) and 8(a)], at the S–S interface, electrons accumulate at the second layer MoS₂ side, and therefore, the energy band of the second layer moves up, leading to a positive band offset (the band offset Δ_CBM = CBM₂ − CBM₁ as shown in the inset of Fig. 7(a). On the contrary, for Mo₂CO₂–BL MoS₂ shown in Figs. 7(b) and 8(b), electrons deplete at the second layer MoS₂ side and a negative band offset is formed. A perfect type II band alignment is demonstrated in these BL MoS₂ homojunctions supported on Mo₂C(OH)₂ and Mo₂CO₂ with the CBM and VBM of the bilayer sharply located at the two different layers of MoS₂.¹⁹ In the Mo₂CF₂–BL MoS₂ junction, the net electron transfer across the M–S interface is negligible, so the electron density redistribution at the S–S interface is also negligible, and hence, the degeneracy in energy of band edges in the two MoS₂ layers is kept [Figs. 8(c) and S4(c) in the supplementary material].

For the S–S interface in the 3D metal Pt(111)–BL MoS₂ junction, a different mechanism appears relative to 2D metal–BL MoS₂ junctions. Figures 7(d) and 8(d) show an opposite direction of dipole at the S–S interface relative to that at the M–S interface. As discussed above [Fig. 5(d)], MIGS appears in the first MoS₂ layer in 3D metal–MoS₂ junction, which means partial metallization of the first-layer of MoS₂. The screening effect occurs in the first-layer of MoS₂ and it tends to screen the dipole at the metal–MoS₂ interface, which is indicated by the arrow in Fig. 7(d). Originated from the screening effect inside the first MoS₂ layer, at the S–S interface, the electrons deplete at the first layer side and accumulate at the second layer side [Figs. 7(d) and 8(d)], which creates an positive band offset and acts as the source of the de-pinning effect between MoS₂ layers.²¹ As a result, the band edges of the second layer MoS₂ is moved up in Pt(111)–BL MoS₂, which leads to the SB-type transition from n-type in Pt(111)–ML MoS₂ [Fig. 3(d)] to p-type in Pt(111)–BL MoS₂ [Fig. 8(d)].

The electron density redistribution at interfaces in Mo₂C(OH)₂-trilayer MoS₂ is also considered in Fig. S7. The electron density distribution at the S^second-layer–S^third-layer interface is the same as that in the S^first-layer–S^second-layer interface but with an even smaller magnitude. Therefore, the electron density redistribution of the third layer and thicker-layers can be inferred to be similar with that in the second layer, and the influence on the MSJ tends to be negligible due to the decay of charge redistribution.

A brief summary for this subsection: the electron density redistributions at the S–S interface inherit the behavior at the M–S interface in 2D metal–BL MoS₂ junctions, while an opposite electron redistribution occurs at the S–S interface relative to that at the M–S interface in 3D metal–BL MoS₂ junctions due to the screening effect of the partially metallized first-layer of MoS₂ and can result in a contact-type-transition from n- to p-type for the junctions with Pt(111).

We have revealed the mechanisms of the electron density redistribution at the M–S and S–S interfaces of bilayer MoS₂ contact to metal electrodes via physisorption. At the M–S interfaces, the pushback effect plays a major role in contacting to 3D metals; charge transfer or polarized covalent-like quasi-bonding appears in 2D metal–MoS₂ junctions as a result of three different types of band alignments from their isolated subsystems. At the S–S interfaces, the electron density redistribution is the same as that at the M–S interfaces for junctions with 2D metals, while an opposite electron density redistribution at the S–S interface from that at the M–S interface is found in junctions with 3D metal. The electron density redistribution at M–S interfaces causes the interface dipole ΔV and ultimately affected the SBH at the M–S interfaces, while the electron density distribution at the S–S interface gives rise to band offset between the semiconducting layers of MoS₂, which may result in a contact-type-transition. Our results offered a comprehensive understanding of the mechanisms of the electron density redistribution at the interfaces between bilayer MoS₂ and 3D/2D metals with a wide-range of work functions, which paves the way to understand and manipulate the performance of metal-2D multilayered semiconductor junctions for electronics and optoelectronics.

See the supplementary material for the reason of using SCAN + rVV10 functional in our manuscript, a list of supercells and lattice mismatch for metal–MoS₂ junctions, and metal work function with strain, figures of the interface potential step and projected band structure of monolayer and bilayer MoS₂ supported on metals, the generation mechanism of the interface dipole at 3D metal–MoS₂ interfaces and charge distribution at Ag–MoS₂ interfaces, electron density redistribution at the MoS₂–MoS₂ interfaces in Mo₂C(OH)₂–trilayer MoS₂ junctions, and the effect of 3R stacking MoS₂.

Q.W., Y.S., and X.S. contributed equally to this work.

The data that support the findings of this study are available within the article and its supplementary material.

This work was financially supported by the Shenzhen Fundamental Research Foundation (Grant No. JCYJ20170817105007999), the Natural Science Foundation of Guangdong Province of China (Grant No. 2017A030310661), and the Guangdong Provincial Key Laboratory for Computational Science and Material Design (Grant No. 2019B030301001). The computational resources were provided by the Center for Computational Science and Engineering of Southern University of Science and Technology.