1 Introduction

As the development of silicon-based transistors has reached the physical limits of silicon-based materials, a simple size reduction is no longer feasible. Researchers are exploring new materials to replace silicon-based materials. Two-dimensional (2D) materials such as graphene [1], boron nitride (BN) [2], transition metal sulfides (TMDs) [3, 4], and transition metal oxides attract more attention due to their unique physical and chemical properties in the fields of field effect transistors, photodetectors, sensors, catalysis, and batteries [5,6,7]. Although graphene has great potential for applications, the inherent zero bandgap limits its application [8]. In contrast, TMDs can be widely used in the field of future nano-electronic devices for their unique optoelectronic properties, for example, limited direct bandgap, large switching ratio, high carrier mobility, and strong optoelectronic effect [9, 10].

Furthermore, the properties of Janus 2D materials by combining different TMDs monolayers are different from those of conventional 2D materials [11,12,13]. Janus 2D material SnXY (X /Y = O, S, Se, Te; X ≠ Y) system showed good electronic and piezoelectric properties [14]. SnSSe is a kinetically and mechanically stable Janus 2D semiconductor with an indirect bandgap [12]. It was found that monolayer (ML) SnSSe has high carrier mobility, high absorption coefficient, high power factor, and strong in-plane piezoelectric polarization, suggesting that Janus ML SnSSe can be fabricated into devices with a unique combination of electronic, optical, piezoelectric, and transport properties [15,16,17].

It is known that Ohmic contact plays a significant role in the performance of the device. However, the existence of the Schottky barrier at the interface between 2D semiconductor materials and metal reduces the carrier transfer efficiency and affects the performance of the device [18]. Because of the metal-induced gap states (MIGS) at the metal–semiconductor contact interface, which leads to the Fermi level pinning (FLP), the potential barrier between the metal and the semiconductor does not change completely with the change of the metal work function. Consequently, it is difficult to achieve Ohmic contact by changing the work function of the metal to match the semiconductor material. There are usually two types of contact between the channels and electrodes in 2D devices, namely surface-contact, and edge contact [19]. The devices with surface-contact have sufficient contact area to achieve low resistance contact. However, due to the van der Waals gap between the electrode and the channel material, the contact resistance increases significantly when the device reaches tens of nanometers [20, 21]. The van der Waals gaps and tunnel barriers are avoided because of the coupling between the metal and the 2D material in an edge-contact device, which achieves small volume and low resistance contact, further reducing transistor size and improving device performance [22,23,24,25,26].

In this work, we systematically explore the electronic properties of the edge-contact heterojunction of SnSSe with the eight metal electrodes (Ag, Al, Au, Cu, Nb, Ni, Ta, and Ti), which is based on density functional theory (DFT) and nonequilibrium Green’s function (NEGF). The calculated results show that an n-type Schottky contact is formed for different heterojunctions with SBH between 0.187 and 0.287 eV. Different interfacial properties of heterojunctions in different transport directions indicate the anisotropy of SnSSe. Moreover, the contact type and SBH can be modulated by the external electric field, and consequently, Ohmic contact can be achieved.

2 Model and calculation details

We select eight common metals Ag, Al, Au, Cu, Nb, Ni, Ta, and Ti as electrodes, and the corresponding lattice mismatches range from 0.30 to 4.80%. Four layers of metal atoms are used to simulate the metal surface. Considering the anisotropy of SnSSe, the heterojunctions of two transport directions are constructed in Fig. 1c, d, respectively. The SnSSe lattice parameter is a = 3.873 Å, which is consistent with previous conclusions [14, 27]. The bond length of the Se–Sn and S–Sn is 2.67 and 2.57, respectively. In addition, the effective masses of electrons and holes are 0.397 m0 and − 0.259 m0, respectively.

Fig. 1
figure 1

a The main view and side view of SnSSe, in which the direction of a is the direction of the armchair and the direction of b is the direction of the zigzag. b Band structure of SnSSe. c Nb/SnSSe/Nb heterojunction in the armchair direction. d Nb/SnSSe/Nb heterojunction in the zigzag direction

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To quantitatively check the thermodynamic stability of SnSSe/metal heterostructures, the binding energies of the heterojunctions are calculated. To quantitatively check the thermodynamic stability of SnSSe/metal heterostructures, the binding energy (∆Eb) is defined as

$$\Delta {E}_{\mathrm{b}}=({E}_{\mathrm{SnSSe}/\mathrm{metal}}-{E}_{\mathrm{SnSSe}}-{E}_{\mathrm{metal}})/n,$$
(1)

where \({\mathrm{E}}_{\mathrm{SnSSe}/\mathrm{metal}}\), \({\mathrm{E}}_{\mathrm{SnSSe}}\), and \({\mathrm{E}}_{\mathrm{metal}}\) represent the total energies of SnSSe/metal, SnSSe, and metal, respectively. n represents the number of atoms [17]. The calculated binding energies are − 0.129 (− 0.199) eV, − 0.101 (− 0.153) eV, − 0.168 (− 0.255) eV, − 0.150 (− 0.596) eV, − 0.092 (− 0.609) eV, − 0.215 (− 0.734) eV, − 0.539 (− 0.700) eV and − 0.349 (− 0.452) eV for Ag, Al, Au, Cu, Nb, Ni, Ta and Ti electrodes along the armchair (zigzag) direction. The negative binding energy of the heterojunction indicates that the heterojunction structures are stable.

All structural relaxation and calculations in this work are performed in Quantum ATK. We use the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) to describe the exchange–correlation potential. The k points are used for the optimization of the structure and the calculations of the electronic transport properties are set to 9 × 9 × 1 and 1 × 9 × 150, respectively. The density mesh cutoff is set to 75 Hartree. The structures are relaxed until the forces of all atoms reached below 0.05 eV/Å. In addition, the electron transport direction is the z-direction. To avoid the interaction between adjacent layers, enough vacuum (20 Å) is added in the x-direction [28].

3 Results and discussion

In Fig. 1a, a direction is the armchair direction and the b direction is the zigzag direction. From Fig. 1b, it can be seen that SnSSe is an indirect bandgap semiconductor with a bandgap of 0.967 eV, which is consistent with the previous report [14, 16, 27]. Figure 1c, d shows the schematic view of the Nb/SnSSe/Nb heterojunctions in the armchair and zigzag directions.

It is known that edge contact between metal and semiconductor can improve contact quality. The reason is that there is a strong interaction between metal and semiconductor at the contact interface, which can improve the electron injection efficiency. To reveal the effect of different metals on electron transport at the contact interface of heterojunctions, we calculate the electron density difference of different heterojunctions. The electron density difference (Δρ) is calculated as follows:

$$\Delta \rho ={\rho }_{\mathrm{metal}/\mathrm{SnSSe}}-{\rho }_{\mathrm{metal}}-{\rho }_{\mathrm{SnSSe}},$$
(2)

where \({\rho }_{\mathrm{metal}/\mathrm{SnSSe} },{\rho }_{\mathrm{metal}}\) and \({\rho }_{\mathrm{SnSSe}}\) are the electron densities of the heterojunction, metal, and SnSSe monolayers, respectively. Negative value of Δρ area indicates the electron depletion region, while positive value of Δρ area represents the electron accumulation region. Charge accumulation and depletion mainly occur near the metal–semiconductor interface, reflecting the charge transfer between the metal and semiconductor. Therefore, we display the electron density difference near the contact interface in Fig. 2. It can been seen that the metal side of all heterojunctions in the armchair direction is the electron depletion region and the SnSSe side is the electron accumulation region, which indicates electrons flow from the metal to the semiconductor SnSSe. However, the metal side of the heterojunctions with the Ag, Al, Au, Cu, and Nb electrodes in the zigzag direction is the electron accumulation region and the semiconductor side is the electron depletion. In this case, the electrons flow from the semiconductor to the metal. While the opposite phenomenon is observed in the heterojunctions with Ni, Ta, and Ti electrodes in the zigzag direction, namely, the electrons flow from the metal to the semiconductor.

Fig. 2
figure 2

The electron density difference of the Ag, Al, Au, Cu, Nb, Ni, Ta, and Ti–SnSSe heterojunction in the armchair (Metal/A-SnSSe) and zigzag (Metal/Z-SnSSe) directions

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To further study the properties of the metal–semiconductor contact interface, we calculate the PDOS of SnSSe in the Ag/SnSSe/Ag heterojunction near the contact interface (nc-SnSSe) and away from the contact interface (c-SnSSe) in Fig. 3. One can see that the bandgap of nc-SnSSe in the heterojunction disappears for the armchair and zigzag directions. Due to the strong orbital overlap between the SnSSe and the metal contact surface, a high-density state is induced in the original bandgap, which makes the nc-SnSSe exhibit metallic properties. This indicates that the SnSSe is metalized at the contact region. However, the PDOS of c-SnSSe in the heterojunction exhibits a significant band gap and still maintains the semiconductor properties.

Fig. 3
figure 3

The partial density of states (PDOS) of SnSSe at the contact interface (nc) and far away from the contact interface (c) in the a armchair and b zigzag directions

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It is known that the SBH affects the performance of the device. The SBH is calculated by the energy difference between the conduction band minimum (CBM) or valence band maximum (VBM) and the Fermi level [29, 30]. The quantum transport simulation includes the coupling between the electrode and the central channel, which is in good agreement with the experiment, so we adopt the method of quantum transport simulation to calculate SBH in this work. Figures 4 and 5 show the local density of states (LDOS) and transmission spectra of the heterojunctions with a channel length of 5 nm at zero-bias and zero-gate voltage. The heterojunctions of metal/SnSSe/metal forms n-type Schottky contact as shown in Table 1. It is found that the different electrodes cause different SBH. Especially, the SBH in the armchair direction is smaller than in the zigzag direction, which suggests the anisotropy of SnSSe. The transport gap is the sum of the electron and hole SBH:

Fig. 4
figure 4

Local density of states (LDOS) and transmission spectrum of SnSSe heterojunctions in the armchair direction under the zero-bias and zero-gate voltage. The Fermi level is at zero energy

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Fig. 5
figure 5

Local density of states (LDOS) and transmission spectrum of SnSSe heterojunctions in the zigzag direction under the zero-bias and zero-gate voltage. The Fermi level is at zero energy

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Table 1 The electron SBH and the transport gap of metal/SnSSe/metal heterojunctions in different directions
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$${{E}}_{\text{g}}^{\text{T}} \, = \, {\phi }_{\text{SB}}^{\text{e}} \, \text{+} \, {\phi }_{\text{SB}}^{\text{h}}.$$
(3)

\({{{E}}_{\text{g}}^{\text{T}}}_{\text{arm}}\) and \({{{E}}_{\text{g}}^{\text{T}}}_{\text{zig}}\) are the transport gap in the armchair and zigzag directions, respectively. One can see that the transport gaps for different heterojunctions are all larger than the band gaps of SnSSe. It suggests that the contact between the SnSSe and metal influences the electronic structure of the semiconductor.

As shown in Figs. 4 and 5, the valence and conduction bands of SnSSe bend upward away from the contact interface. Because the charge is redistributed due to the metal–semiconductor contact, which leads to the upward bending of the conduction and valence bands. The strong MIGS are apparent in the contact interfaces, as shown by yellow double-headed arrow in Figs. 4 and 5. MIGS will shorten the effective channel length, serve as the source for electrons or holes, and induce a FLP. FLP not only causes the increased the SBH, but also makes the SBH difficult to modulate by a gate voltage, which influences the device performance [31]. The MIGS of heterojunction in the armchair direction are weaker than in the zigzag direction. Moreover, the heterojunctions with Nb, Ni, Ta, and Ti electrodes exhibit stronger MIGS in the armchair direction. In the zigzag direction, the heterojunctions with Ag, Al, Au, Cu, and Ni electrodes show weaker MIGS, while the heterojunctions with Nb, Ta, and Ti electrodes show stronger MIGS. A weaker MIGS indicates better electric field modulation performance.

As we know, MIGS induce FLP at the contact interface, affecting gate regulation of the heterojunction. When MIGS is weak, SBH is significantly affected by the external electric field, so it is possible to tune the SBH of heterojunction by changing the external electric field. In Figs. 4 and 5, there are few MIGS in Cu/SnSSe/Cu heterojunction with low SBH in both transport directions. The Ti/SnSSe/Ti heterojunction presents more significant MIGS. The Nb/SnSSe/Nb heterojunction shows significant anisotropy. Therefore, we choose these three heterojunctions to understand the effect of external electric fields on metal/SnSSe/metal heterojunctions as shown in Fig. 6. From Fig. 6, one can see that the SBH changes significantly as the external electric field increases from − 1.5 to 1.5 V/nm. The SBH in the Cu/SnSSe/Cu heterojunction in the two transport directions has little difference under the external electric field, whose changing trends are the same, and the contact type remains unchanged. The Ohmic contact is achieved when the external electric field is larger than 0.5 V/nm. For Nb/SnSSe/Nb heterojunction in armchair direction, Ohmic contact is achieved when the electric field is larger than 0.5 V/nm, and the Schottky contact type changes from n-type to p-type between − 1 and − 1.5 V/nm. When the electric field is larger than 1 V/nm, the heterojunction with the Nb electrode in the zigzag direction realizes Ohmic contact and the Schottky contact type changes to p-type between − 1 and − 0.5 V/nm. For the Ti/SnSSe/Ti heterojunction, the change of Schottky contact is similar to the Nb/SnSSe/Nb heterojunction, and its Schottky contact type changes under electric fields of − 0.5 to 0 V/nm in both transport directions. It is worth noting that for the Ti/SnSSe/Ti heterojunction in the zigzag direction, the Ohmic contact cannot be achieved in our selected electric field interval, which is consistent with the above conclusion that the FLP at the contact interface of the Ti heterojunction is significant. To further understand the variation of the Schottky barrier under the external electric field, we calculate the electron density difference of the Ti/SnSSe/Ti heterojunction. In Fig. 6d, it can be seen that the external electric field causes the varied charge transfer at the contact interface, thereby affecting the Schottky barrier of heterojunction.

Fig. 6
figure 6

The trend of SBH with the electric field of a Cu/SnSSe/Cu, b Nb/SnSSe/Nb, and c Ti/SnSSe/Ti heterojunctions. d The electron density difference of Ti/SnSSe/Ti heterojunction under different external electric fields in the armchair and zigzag directions

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Figure 7a–e shows the LDOS of Cu/SnSSe/Cu, Nb/SnSSe/Nb heterojunctions in two transport directions and Ti/SnSSe/Ti heterojunction in the armchair direction. The CBM of the metal/SnSSe/metal heterojunction crosses the Fermi level under the external electric field, indicating that Ohmic contact is formed between the metal and the semiconductor, and electrons can easily transfer from the metal electrode to the SnSSe. Figure 7f shows that the CBM of the Ti/SnSSe/Ti heterojunction in the zigzag direction is close to the Fermi level under an electric field of 1.5 V/nm, but the Ohmic contact is not formed. From Fig. 7g, h, the VBM of the Ti/SnSSe/Ti heterojunction is close to the Fermi level, suggesting a p-type Schottky contact characteristic under the external electric field of − 1.5 V/nm. Furthermore, the band-bending phenomenon is more obvious under the negative external electric field, which corresponds to the more charge transfer in Fig. 6d. The electric field affects the charge transfer between the metal and the semiconductor, thereby changing the built-in electric field [32]. Thus, CBM and VBM move compared with the zero electric field, resulting in the changed height of the Schottky barrier [33,34,35].

Fig. 7
figure 7

The LDOS of three heterojunctions in the armchair and zigzag directions under different external electric fields

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Figure 8 displays the transmission eigenstates (ES) of the Ti/SnSSe/Ti heterojunction in the armchair direction under V = 0.0 V/nm and V = 1.0 V/nm. The incident wave function of the eigenstate is localized at the source under zero external electric field. When the external electric field increases to 1.0 V/nm, the incident wave function of the eigenstate is delocalized on the whole device. Therefore, the Ohmic contact induced by the electric field causes better electronic transport. The external electric field not only induces the transition from the n-type Schottky contact to the p-type Schottky contact but also modulates the SBH to achieve the Ohmic contact. These results suggest that the electric field is an effective way to control Schottky contact in metal/SnSSe/metal heterojunctions, providing a promising possibility for designing tunable Schottky devices by modulating electric fields.

Fig. 8
figure 8

Comparison of the transmission eigenstates (ES) of the Ti/SnSSe/Ti heterojunction in the armchair direction under different external electric fields

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4 Conclusions

We have investigated the interfacial properties of metal/SnSSe/metal heterojunctions in the armchair and zigzag directions using DFT and NEGF. The heterojunctions exhibit different electronic properties in different transport directions, which suggests the anisotropy of SnSSe. The SnSSe-based heterojunctions with eight metals form an n-type Schottky contact in different transport directions and the SBH are 0.187–0.287 eV. The SBH of heterojunctions in the armchair direction is generally smaller than that in the zigzag direction. In the selected case of the heterojunctions with Cu and Nb electrodes, the ohmic contact is achieved under an external electric field in two transport directions, showing better electronic transport. Especially, the Ti/SnSSe/Ti heterojunction cannot form the ohmic contact in the zigzag direction because of strong MIGS at the contact interface. The result indicates that SnSSe-based heterojunction with metal can become a candidate for an electronic device with tunable Schottky contact.