Introduction

Over the past decades, the performance of silicon as a channel material for field-effect transistors has reached a limit. Due to short channel effects at scales below 3 nm and further bottlenecks, alternative channel materials need to be explored1,2,3,4,5. Due to their high stability6,7 and suitable band gap8, two-dimensional (2D) transition-metal dichalcogenides are of particular interest9,10. The family of 2D transition-metal dichalcogenides also comprises Janus materials11, such as MoSSe, which are special because their structural asymmetry introduces an electric dipole12,13. This dipole may affect the contacts between the channel material and metallic electrodes, which are critical for the device performance14,15.

To achieve an ohmic contact, the barrier height of a Schottky semiconductor-metal contact is commonly regulated to zero by selecting a metal with an appropriate work function16. Regrettably, Fermi level pinning hinders this regulation and thus compromises electron transport17. Bulk metals often generate metal-induced gap states18 and strong contact interactions due to dangling bonds19, which both enhance Fermi level pinning20. To address these issues, the thickness of the metal can be reduced to the nanoscale21,22, and buffer layers can be added23,24. Alternatively, the semiconductor can be placed in contact with a 2D metal25,26,27,28,29,30 to form weakly interacting van der Waals contacts and simultaneously reduce the device size31,32,33. However, it is not known how the electric dipole of a Janus semiconductor employed as a channel material influences the properties of van der Waals contacts. For this reason, we study the electronic properties of contacts formed between Janus MoSSe and 2D metals. In particular, we demonstrate suppression of the Fermi level pinning and formation of ideal ohmic contacts.

Computational methods

All calculations are performed using the projector-augmented wave method of the Vienna ab initio simulation package34 with a 500 eV plane wave energy cutoff. A dipole correction is added for each of the studied systems. The optB88-vdW functional is adopted to accurately model the van der Waals interaction35,36, as it reliably describes 2D layered systems37. The band structure and work function are evaluated using the hybrid Heyd-Scuseria-Ernzerhof functional38. We set the convergence criteria to 10−5 eV for the total energy and to 0.01 eV/Å for the maximal residual force. Vacuum layers of 20 Å thickness are added to the structure models to ensure that artificial interaction does not occur in the out-of-plane direction due to the periodic boundary conditions. A Monkhorst-Pack k-grid with a separation of 0.015 to 0.020 Å−1 between the grid points is employed. Electronic transport calculations are performed using the nonequilibrium Green’s function method of the Quantum ATK package39 with norm-conserving pseudopotentials (300 Ry energy cutoff). A Monkhorst-Pack 1 × 5 × 100 k-grid is employed for the semi-infinite electrode calculations, and a Monkhorst-Pack 1 × 5 × 1 k-grid is employed for the transport calculations.

We study graphene and silicene as classical group-IV 2D metals and M3C2 (M = Zn, Cd, Hg) as a new class of promising 2D Dirac metals40. Based on the structure of MoSSe, we further select metallic 1T- and 2H-phase transition-metal dichalcogenides XA2 with X = Nb, Ta and A = S, Se, Te. The unit cells of all the 2D metals are presented in Fig. 1. Contacts between the S- and Se-sides of MoSSe with the 2D metals are considered, which are referred to as SeMoS/metal and SMoSe/metal contacts, respectively. The in-plane lattice constants of the contact structure models are set to the average of the component’s lattice constants, and the lattice mismatch is minimized by the following supercells (remaining lattice mismatch given in brackets): √7 × √7 × 1 graphene (0.4%), √3 × √3 × 1 silicene (3.3%), and 1 × 1 × 1 Zn3C2 (0.1%) on 2 × 2 × 1 MoSSe; √3 × √3 × 1 Cd3C2 (4.6%) and √3 × √3 × 1 Hg3C2 (5.6%) on 4 × 4 × 1 MoSSe; 1 × 1 × 1 NbS2 (2H: 3.0%), NbSe2 (2H: 6.8%), TaS2 (1T: 3.9%; 2H: 2.8%), and TaSe2 (2H: 6.6%) on 1 × 1 × 1 MoSSe; √7 × √7 × 1 TaTe2 (1T: 0.3%; 2H: 0.6%) on 3 × 3 × 1 MoSSe.

Fig. 1: Structure.
figure 1

Top and side views of (a) the unit cells for the considered metals and (b) the SeMoS/metal contact.

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Results and discussion

Due to the asymmetry of Janus MoSSe, the properties of both the S- and Se-sides are examined. The binding energy of a contact is calculated as Eb = (Econtact ‒ EMoSSe ‒ Emetal)/A, where Econtact, EMoSSe, and Emetal are the total energies of the contact, isolated MoSSe, and isolated metal, respectively. Moreover, A is the contact area, which is used for normalization. For each contact, the obtained values of Eb and the interlayer spacing d are shown in Table 1. For contacts with both the S- and Se-sides, Eb is highest for XA2 (except for TaTe2), intermediate for group-IV 2D metals, and lowest for M3C2. For group-IV 2D metals and M3C2, the S-side provides a higher Eb than the Se-side, which is consistent with previous results for the contact between MoSSe and germanene41. 1T-XA2 exhibits the same trend, while 2H-XA2 exhibits the opposite trend. As the value of d always falls within 2.9 to 3.6 Å, no chemical bonds are formed at the contact. As expected, d is smaller for the SeMoS/metal contacts than for the SMoSe/metal contacts. To enable quantitative comparison, we calculate the charge transfers Δq (Bader scheme) across the contact normalized by A, as shown in Table 1. Positive (negative) values represent forward (backward) charge transfer from the metal to MoSSe (from MoSSe to the metal). While all the values remain close to zero, the forward (backward) charge transfers at the SMoSe/metal contacts are systematically damped (enhanced) compared to the SeMoS/metal contacts.

Table 1 Absolute binding energy (|Eb|), contact spacing (d), charge transfer across the contact (Δq), and n/p-type Schottky barrier height (Φn/Φp) of SeMoS/metal and SMoSe/metal contacts.
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The weighted band structures in Fig. 2a demonstrate that the SeMoS/Zn3C2 contact is ohmic and thus superior to the n-type SeMoS/silicene (Φn = 0.10 eV) and SeMoS/1T-TaS2 (Φn = 0.09 eV) contacts, where Φ is the Schottky barrier height (SBH). While the SeMoS/Cd3C2 and SeMoS/Hg3C2 contacts develop finite band gaps (due to the sizable lattice mismatch and induced in-plane strain in these cases), the Dirac cone of the SeMoS/Zn3C2 contact at the Fermi level enables efficient charge transport. According to Table 1, the SeMoS/metal contacts tend to be n-type with sufficiently small SBHs. The SMoSe/Zn3C2 and SMoSe/2H-TaS2 contacts are ohmic, as shown in Fig. 2b, and according to Table 1, for the other SMoSe/metal contacts, the n-type SBHs tend to be larger than the p-type SBHs. Regardless of the termination, n-type contacts are formed with the group-IV 2D metals, and ohmic contacts are formed with Zn3C2. In contrast, contacts with XA2 behave differently for the two terminations, as the S-side tends to form n-type contacts and the Se-side tends to form p-type contacts.

Fig. 2: Electronic states.
figure 2

Weighted band structures of the (a) SeMoS/metal and (b) SMoSe/metal contacts. The orange and purple colors denote the contributions of MoSSe and the metal, respectively.

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The work functions of the considered 2D metals (Wmetal) fall within 4.31 to 6.01 eV, and their Fermi levels (EF) are located within the band gap of MoSSe (see the red horizontal lines in Fig. 3a). While the group-IV 2D metals and M3C2 have low work functions, 2H-TaS2, 2H-NbS2, and 2H-NbSe2 are characterized by high work functions. Compared to the 2D metals, EF changes little or shifts to higher energy (with respect to the vacuum level) for the SeMoS/metal contacts, while it shifts to lower energy for the SMoSe/metal contacts. This explains why the S-side (Se-side) tends to form n-type (p-type) contacts. For growing Wmetal, the character of the contact evolves from n-type to p-type. In Fig. 3a, the highest occupied and lowest unoccupied states of MoSSe in the contact are marked above and below EF (except for the Cd3C2/metal and Hg3C2/metal contacts with finite band gaps). For the ohmic contacts, only EF is shown. Note that Wmetal refers to the strained metals. For 2H-NbSe2 and 2H-TaSe2 (which exhibit a large lattice mismatch), the strain alters Wmetal by only 0.24 and 0.23 eV, respectively, which demonstrates the robustness of our conclusions in combination with the knowledge that the band gap of MoSSe is altered by only 0.40 eV under 3% strain42.

Fig. 3: Work functions and SBHs.
figure 3

(a) Work functions before and after contact formation. Ec denotes the conduction band edge, and Ev denotes the valence band edge of MoSSe. SBH versus work function for the (b) SeMoS/metal and (c) SMoSe/metal contacts.

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The SBH is very sensitive to Wmetal according to the Schottky-Mott rule18, which, however, is of limited validity in the case of Fermi level pinning. The pinning factor S = |dΦ/dWmetal| measures the shift of the Fermi level of a semiconductor/metal contact when different metals are used. For S = 0, the Fermi level is fully pinned, while for S = 1, the Schottky–Mott limit is achieved. As shown in Fig. 3b, c, sizable values of S = 0.86 and S = 0.81 are obtained for contacts with the S-side and Se-side, respectively, implying that 2D metals are superior to bulk metals for contacting Janus MoSSe (even though both realize weak binding), especially for the S-side (S = 0.28)43. Due to the excellent values of S, it is expected that the Fermi level pinning will be weak.

While contacts with weak binding have the advantage of reducing the Fermi level pinning, the tunnel barrier can be an issue44. Figure 4a displays the electrostatic potential of the SeMoS/graphene contact with the tunnel barrier height ΦTB = Φgap − ΦMoSSe being the difference between the potential maxima of the contact (Φgap) and the termination layer of MoSSe (ΦMoSSe). The tunnel barrier width WTB refers to ΦMoSSe. On the other hand, ΦTB = Φgap − Φmetal, and WTB refers to the potential minimum of the metal (Φmetal) when Φmetal > ΦMoSSe. Low ΦTB and low WTB, which correspond to the bottom left corner of Fig. 4b, imply enhanced tunneling. Figure 4b indicates that there are four groups of contacts. The contacts with XA2 constitute Groups 1 and 3, where Group 3 consists of all the contacts involving TaTe2 and combines low binding energy with rather low ΦTB. The contacts with group-IV 2D metals constitute Group 2, which is the least competitive. The two ohmic contacts with Zn3C2, which constitute Group 4, achieve the lowest ΦTB but suffer from the highest WTB, while the ohmic contact SMoSe/2H-TaS2 combines low ΦTB = 8.94 eV with the lowest WTB = 1.91 Å of all contacts under investigation.

Fig. 4: Electrostatic potential and tunnel barrier height.
figure 4

(a) Electrostatic potential (including the exchange potential) versus z-position for the SeMoS/graphene contact. (b) Tunnel barrier height versus tunnel barrier width. Numerical values are provided in Table 2.

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Considering the inherent dipole moment of Janus materials, we next quantify the induced dipole moment of the contact. Figure 5 shows schematic diagrams of the relationship between the total dipole moment of the contact (Dtot) and the interfacial dipole moment (Dint). Two (three) classes of patterns are found for the contacts with the S-side (Se-side). The obtained values of Dtot and Dint are shown in Table 2, in which the positive (negative) sign corresponds to the direction from the 2D metal (Janus MoSSe) to Janus MoSSe (the 2D metal). Dtot is always negative for contacts with the S-side (classes I and II), i.e., it inherits the direction of the dipole moment of Janus MoSSe (DMoSSe). Although charge transfer occurs across the contact (Table 1), the amount is not sufficient to change the direction of Dtot. The SeMoS/M3C2 contacts show the least negative values. The interfacial dipole moment Dint = (Dtot - DMoSSe)/N, where N denotes the number of unit cells of MoSSe in the supercell, may be negative (class I; Dtot is more negative) or positive (class II; Dtot is less negative). Given that Dtot inherits the direction of DMoSSe, we expect Dtot to be positive for the SMoSe/metal contacts, which is true in most cases (classes III and IV). The only exceptions are the SMoSe/2H-TaS2 and SMoSe/2H-NbS2 contacts (class V), in which a considerable charge transfer from Janus MoSSe to the 2D metal leads to a negative Dtot and to a significantly negative Dint, resulting in a favorable ohmic behavior of the SMoSe/2H-TaS2 contact and a tiny Φp = 0.08 eV of the SMoSe/2H-NbS2 contact.

Fig. 5: Dipole moment.
figure 5

Schematic diagrams of the (a) SeMoS/metal and (b) SMoSe/metal contacts.

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Table 2 Tunnel barrier height (ΦTB) and width (WTB), total (Dtot) and interfacial (Dint) dipole moments, and classes of SeMoS/metal and SMoSe/metal contacts.
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The transmission coefficient \(T={\left(1+\frac{{\sinh}^{2}\left(\sqrt{2m{\Phi }_{{\rm{TB}}}(1-E/{\Phi }_{{\rm{TB}}})}{W}_{{\rm{TB}}}/{{\hbar }}\right)}{4E/{\Phi }_{{\rm{TB}}}\left(1-E/{\Phi }_{{\rm{TB}}}\right)}\right)}^{-1}\), where E is the energy and m is the mass of the electron, is shown in Fig. 6a–d for representative contacts from the groups in Fig. 4b. In each case, T ~ 1 already at E/ΦTB ≲ 2. Consistent with the previous discussion, T tends to be slightly higher for Se than for S termination at low energy. A comparison of the low energy range is given in Fig. 6e for the contacts with the Se-side, showing that 2H-TaS2 and 2H-TaSe2 (contacts located in the left bottom corner of Fig. 4b) result in slightly higher T. Adopting the device model of Fig. 6f, electronic transport calculations are performed for the ohmic SMoSe/2H-TaS2 contact using channel lengths of 20.96, 26.67, and 32.67 Å. The obtained I-V curves in Fig. 6g demonstrate an ohmic behavior, particularly for a channel length of 20.96 Å. We use the transfer length method to extract the specific contact resistance. As the total resistance is 2R1 + R2, as shown in Fig. 6f, the crossing point between the total resistance axis and the linear fit of the obtained total resistances in Fig. 6h is 2R1. After R1 is multiplied with the width w = 13.18 Å, a specific contact resistance of 97.5 Ωµm is obtained.

Fig. 6: Transmission and Transport.
figure 6

Transmission coefficients of the contacts of MoSSe with (a) graphene, (b) Zn3C3, (c) 2H-TaS2 and (d) 2H-TaTe2. (e) Comparison of the results in (a–d) for E/ΦTB ≤ 1. (f) SMoSe/2H-TaS2 device model (electrodes saturated by H atoms) used for the electronic transport calculations. (g) I-V curve for different channel lengths. (h) Linear fit of the obtained total resistances.

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Conclusions

Our first-principles study on the interaction between Janus MoSSe and various 2D metals shows that both the S- and Se-sides of Janus MoSSe can form ohmic contacts, as desired for electronic devices. Promising Fermi level pinning factors of 0.86 (S-side) and 0.81 (Se-side) are obtained, which reduces the Fermi level pinning. Among the studied 2D metals, Zn3C2 gives rise to the best contacts for both terminations of Janus MoSSe, as they are ohmic and the tunnel barriers are low (7.60 and 7.46 eV, respectively). Through its interfacial dipole moment, the SMoSe/2H-TaS2 contact is also ohmic. Our work provides theoretical support for the application of Janus MoSSe as a channel material in nanoelectronics by identifying suitable 2D electrode materials. These 2D electrodes will not only improve the performance but also reduce the thickness of the device.