# Titanium disulfide as Schottky/ohmic contact for monolayer molybdenum disulfide

Jul 31, 2020

### TiS2 contact formation with ML MoS2

The “Methods” section describes the density functional theory (DFT) techniques used for this research. The contact formation between TiS2–MoS2 leads to two interfaces as seen in Fig. 2d. To confirm this, two geometries are adopted to investigate the contact, which are shown in Fig. 2a, b. A group of TiS2–MoS2 junctions are used to test the electron transport from TiS2 contact to the ML MoS2 sheet at the lateral interface (interface A in Fig. 2d). Another group of FET-like TiS2–MoS2 heterostructures (TiS2–MoS2 FET-like junctions) are used to simulate the electron transportation from the contact region to semiconducting channel region at the vertical interface (interface B in Fig. 2d).

For TiS2–MoS2 FET-like junction, the PLDOS is calculated for revealing the band structure after the contacting of 1–4 layers of TiS2 and ML MoS2 sheet. The configuration after geometrical optimization (GO) is shown by Fig. 2d. The overlap of 1–4 layers of TiS2 and ML MoS2 is 2.5 nm. Due to the limitation of computational capability, the ML-MoS2 channel is set as 8 nm. To increase the accuracy in the transportation direction, the k-point sampling is changed to 10 × 1 × 40. For each of 1–4 layers of TiS2 simulations, The MoS2 channel doping is varied to understand the type of electrode formation as 5 × 1018 cm−3 (3.25 × 1011 cm−2 for ML MoS2) n-type doping, 1 × 1019 cm−3 (6.5 × 1011 cm−2 for ML MoS2) n-type doping, 5 × 1019 cm−3 (3.25 × 1012 cm−2 for ML MoS2) n-type doping, and 5 × 1018 cm−3 (3.25 × 1011 cm−2 for ML MoS2) p-type doping. Thus, we obtain a ni value of 1.4 × 104 cm−3 for ML MoS2. We chose the doping concentration carefully to meet the calculated upper and lower limits: a large doping concentration will lead to degenerate behavior of the channel and a small doping concentration will cause the depletion length to exceed the length of channel creating artificial results. The overlap region between the TiS2 and MoS2 is undoped. Only the uncovered ML-MoS2 channel is doped with the chosen doping concentrations.

To investigate the charge transport and its mechanism through the interface A in Fig. 2d, the calculation of DOS, ED, average binding energy (EBE), and EDP are conducted after the GO.

After simulating the DOS of the optimized TiS2–MoS2 structure, the projected partial DOS (PDOS) is shown in Fig. 3. The PDOS of TiS2 after making contact with ML MoS2 is shown in Fig. 3a–d for one–four layers of TiS2. It shows that, after making a contact with ML MoS2, the TiS2 DOS remains the same as the free-standing TiS2. The only difference is that some trap states are added which shown as spikes in Fig. 3a–d. These added states are created by the tiny displacement of the atoms in TiS2 layer, which is of the order of 0.01 Å. This indicates that the presence of ML MoS2 has a negligible effect on the TiS2 band structure. The situation of MoS2 is different, as shown in Fig. 3e–i which show the PDOS of ML MoS2 after making contact with one–four layers of TiS2. The plot clearly demonstrates that the TiS2 contact modifies the MoS2 band structure significantly and adds a large amount of p-type doping to the ML MoS2. In Fig. 3e–i, compared with the band structure and DOS of intrinsic ML MoS2 on the left side, for all the cases of ML to four-layer TiS2 contacts, the PDOS of ML MoS2 exhibits Fermi level pinning towards valence band. This shift of Fermi level ranges from 0.40 to 0.45 eV. Even though the three-layer and four-layer TiS2 forming a contact with ML MoS2 show a larger Fermi level shift, the difference in Fermi level shift with change in number of TiS2 layers is very small. The energy difference between the valence band and Fermi level is 0.05–0.1 eV. The energy difference between the Fermi level and valence band is defined by

$$varPhi = E_{mathrm{f}} – E_{mathrm{V}},$$

(1)

where (E_{mathrm{f}}) and (E_{mathrm{V}}) are the Fermi level and the valence band top, respectively. Knowing the Fermi level shift and (varPhi), the p-type doping concentration can be determined by calculating the effective DOS in the conduction band ((N_{mathrm{c}})) and the valence band ((N_{mathrm{v}})). As there are not too many reported values of Nc and Nv reported, we have calculated these to estimate what doping concentration we should use for our electrode simulations for ML MoS2. Hence, the effective density of state values is required only for estimating the doping concentrations of MoS2. After simulating the DOS, the energy difference between the quasi-Fermi level and the valence band can be calculated. These two well-defined equations can be applied to determine (N_{mathrm{c}}) and (N_{mathrm{v}}):

$$N_{mathrm{c}} = nexp left( {frac{{E_{mathrm{c}} – E_{mathrm{F}}}}{{kT}}} right),$$

(2)

$$N_{mathrm{v}} = pexp left( {frac{{E_{mathrm{F}} – E_{mathrm{v}}}}{{kT}}} right),$$

(3)

where n and p are the electron and hole concentrations, respectively. k is Boltzmann constant and T is temperature in K. From the simulation, (N_{mathrm{c}}) and (N_{mathrm{v}}) for ML MoS2 are calculated to be 2 × 1019 cm−3 (1.38 × 1012 cm−2) and 1 × 1019 cm−3 (6.5 × 1012 cm−2), respectively, which are similar to the reported ML and bulk MoS2 values36,37,38,39. Using these values, the calculated doping concentration added to the ML MoS2 by TiS2 contacts with different number of layers ranges from 3.85 × 1017 to 2.63 × 1018 cm−3 (2.50 × 1010 to 1.71 × 1011 cm−2 for ML MoS2). Compared with metal–MoS2 contacts14,15,16,17,18, although the ML MoS2 is p-type doped after forming a contact with TiS2, its bandgap is preserved as shown in Fig. 3e–i; in contrast, the metal contact will metalize the ML MoS2 and fill its bandgap with states as shown in Fig. 1a. The TiS2–MoS2(ML) contact makes ML MoS2p-type as compared to the n-type in graphene–MoS2 contact (Fig. 1b).

Thus, the DOS simulation indicates that TiS2–MoS2 (ML) contact is a unique contact with less metallization and p-type behavior. It is necessary to conduct a comprehensive analysis on its interfacial bonding condition. ED and EBE are two important criteria to evaluate the bonding between TiS2 and ML MoS2. The average binding energy (EBE), EB, can be defined as

$$E_{mathrm{B}} = left( {E_{mathrm{T}} + E_{mathrm{M}} – E_{{mathrm{T}} – {mathrm{M}}}} right)/N,$$

(4)

where (E_{mathrm{T}}) is the total energy of the free-standing TiS2, (E_{mathrm{M}}) is the total energy of the intrinsic ML MoS2, (E_{{mathrm{T}} – {mathrm{M}}}) is the total energy of the TiS2–MoS2 (ML) contact after GO, and N can be considered as the number of interfacial sulfur atoms on the MoS2 side.

The ED of the TiS2–MoS2 junctions are shown by Fig. 4a–d for one–four layers of TiS2. As seen in the plot, there is a clear gap between the TiS2 layer and MoS2 with no charge distribution in it. The overlap of the electron gas between TiS2 and MoS2 is very limited, as can be observed from the contour plot. The plot of the projected electron density (ED) in the y direction also clearly shows that the ED overlap at the contact interface is very similar to those between TiS2 layers, indicating that the bonding between TiS2 and MoS2 is not much stronger than interfacial bonding within TiS2 layers. The buckling distance can also be extracted from both the ED plot and GO. For TiS2–MoS2(ML) junctions, the optimized buckling distance for TiS2–MoS2 contacts are: 3.2282 Å for TiS2(ML)–MoS2(ML), 2.8112 Å for TiS2(2L)–MoS2(ML), 2.8069 Å for TiS2(3L)–MoS2 (ML), and 2.7381 Å for TiS2(4L)–MoS2(ML). For comparison, the inter-layer distance for TiS2 and MoS2 is 2.8678 and 2.9754 Å, respectively. It is clear that thicker TiS2 has larger attractive force to ML MoS2 and leads to smaller inter-layer distance. These ED results reveal that the bonding between the TiS2 contact and ML MoS2 in TiS2–MoS2 (ML) junctions is Van der Waals bonding. Unlike the covalent bond, the delocalization of interfacial electron gas would not exist in these cases.

By using this definition, the EBE for TiS2–MoS2(ML) interface is 0.7426 eV, while this value is 0.7157 eV for the Van der Waals bonds of bilayer MoS2. This result further confirms the previous results and demonstrates that TiS2–MoS2 (ML) contact is a Van der Waals contact.

The tunneling barrier at the TiS2–MoS2 (ML) interface will determine the charge transport through the interface A. To evaluate the impedance to the current transportation added by the tunneling barrier, the electrostatic difference potential (EDP) of the TiS2–MoS2 contact is simulated. As shown in Fig. 4e, the potential between the TiS2 and MoS2 is considered as the tunneling barrier. The shape of the potential barrier can be estimated as a rectangle. The tunneling probability, from the TiS2 to the ML MoS2 can be defined as, of carriers tunneling through the barrier, TB

$$T_{mathrm{B}} = {mathrm{exp}}left( { – 4{pi }frac{{sqrt {2{m}Delta {V}} }}{{h}}W_{mathrm{B}}} right),$$

(5)

where (Delta V) is the barrier height, which is defined by the length of the rectangle, h is the Planck constant, and (W_{mathrm{B}}) is the barrier width, which is defined as the half width of the rectangle. (Delta V) and (W_{mathrm{B}}) can be directly extracted from Fig. 4e: (Delta V) is 0.404620 eV and (W_{mathrm{B}}) is 0.35412 Å. By using these parameters and Eq. (4), we calculate (T_{mathrm{B}}) as 79.4%. A large (T_{mathrm{B}}) indicate small impedance and a higher charge injection. It is very clear that even though the tunneling barrier at the interface A resists the charge transport vertically through the interface, the possibility of tunneling is high for carriers because of a very tiny barrier width (0.35412 Å). For this reason, the charge injection at the lateral interface can be ignored. However, the interfacial tunneling barrier within the TiS2 contact may scatter the electrons and holes. This scattering effect can be reduced by using a thinner TiS2 film. Thus, we also address scaling down the thickness of TiS2 contacts after meeting the stability requirement.

By analyzing the ED, EBE, and GO for configuration for interface A, it can be concluded that TiS2 tends to form Van der Waals bond with ML MoS2, with thicker TiS2 creating stronger bonding. The DOS in Fig. 3 shows that less metallization is created due to the weak Van der Waals bonding and the bandgap of ML MoS2 is preserved. DOS results also show that TiS2 will add p-type doping to the ML MoS2. The EDP results in Fig. 4 show that the tunneling barrier is small at interface A, which means that the current injection would not be seriously impeded.

To understand the source-to-channel/channel-to-drain working mechanism for the TiS2–MoS2 (ML) contacts applied in 2D FET, the PLDOS is adopted to sketch out the framework of the band structure at the interface B of the TiS2–MoS2 FET-like junctions. The PLDOS uses a contour plot to map the DOS projected onto the c-axis, which is the transportation direction. The band structure can be determined by plotting the boundary between the states-filled region (bright region) and the no-states region (dark region). The extraction of the barrier height and contact type of TiS2–MoS2 contact can be achieved by evaluating the PLDOS. Two reasons let us dope the ML MoS2. First, the intrinsic carrier concentration of ML MoS2 is small; therefore, it is a good choice to dope the MoS2 channel to improve the conductivity. For this reason, it is of great interest to investigate the contact consisting of doped ML MoS2. Also, the channel length is set to 8 nm based on computational considerations, as mentioned earlier. An adequate amount of doping concentration is required to make sure that the depletion length is smaller than the channel length of the simulated configuration. Although the barrier height and contact type for the contact of intrinsic ML MoS2 and TiS2 cannot be extracted directly from the PLDOS, but the barrier height and contact type of doped cases can still be extracted accurately.

### MoS2 doping-dependent contact formation with TiS2

Four different doping concentrations: 5 × 1018, 1 × 1019, and 5 × 1019 cm−3n-type doping and 5 × 1018 cm−3p-type doping is tested. The simulation results are shown in Table 1. Figure 5 shows only the results of the TiS2(4L)–MoS2(ML) cases and the variation of the band structures with different doping concentrations.

For n-type doping concentrations smaller than (N_{mathrm{c}}), the Schottky barrier height of the contacts are large: 1.03–1.07 eV for 5 × 1018 cm−3, and 0.88–0.95 eV for 1 × 1019 cm−3, as shown in Table 1 and Fig. 5b, c. Table 1 also clearly shows that for the cases with ML TiS2, ({varPhi }_{p}) of the contact is larger than ({varPhi} _{p}) of 2L–4L cases with the same doping concentration. For the n-type doping concentration of 5 × 1018 cm−3, ({varPhi}_{p}) is 0.67 eV for ML but 0.21–0.25 eV for 2–4L. For n-type doping concentration of 1 × 1019 cm−3, ({varPhi}_{p}) is 0.7 eV for ML but 0.40–0.44 eV for 2–4L. By summing ({varPhi}_{n}) and ({varPhi}_{p}), the modified (E_{mathrm{g}}) is 1.70 eV for the ML case doped n-type with concentration 5 × 1018 cm−3, and for 2–4L cases doped with this concentration, ({E}_{mathrm{g}}) ranges from 1.26 to 1.32 eV. For n-type doping of concentration 1 × 1019 cm−3, (E_{mathrm{g}}) is 1.65 eV for ML and 1.32 eV for 2–4L.

For a larger n-type doping concentration (5 × 1019 cm−3), as shown in both Table 1 and Fig. 5a, the Schottky barrier height is 0.30–0.45 eV, which is much smaller than the cases with n-type doping concentrations of 5 × 1018 and 1 × 1019 cm−3. This reduction in barrier height may be brought about by multiple causes. One possible reason is the imaging force created by the larger amount of excess charge, as a result of the larger doping concentration. It is observed that ({varPhi}_{p}) increases compared with lower doping concentrations. ({varPhi}_{p}) is 0.92–0.97 eV for the 1–4L cases. (E_{mathrm{g}}) for this concentration is 1.27–1.37 eV.

The simulation results and mapped band structures in Fig. 5a–c for n-type-doped TiS2–MoS2(ML) contacts show that, normally, n-type-doped TiS2–MoS2(ML) contacts show a large barrier height, which is around 1.0 eV below a degenerate doping. Even though Fig. 5 shows that a larger doping concentration will reduce the barrier height for n-type carriers, it is obvious that, even for a doping concentration very close to degeneration, the Schottky barrier height is still larger for TiS2–MoS2(ML) contacts. The inference from Fig. 5 is that since the majority carriers in these n-type-doped contacts are always faced with a large Schottky barrier height, the n-type-doped TiS2–ML MoS2 Schottky diodes can probably act as high-power switches or Schottky barrier MOSFETs based on tunneling.

Unlike the n-type contacts, the p-type-doped TiS2–MoS2(ML) contacts shows zero barrier height when the p-type doping concentration reaches 5 × 1018 cm−3. In Fig. 5d, it is observed that, at this doping concentration, the depletion width vanishes and the band is flat. The Schottky barrier at the interface shows both a small barrier height and a small built-in potential, which indicates the contact is an ohmic contact for ML MoS2-doped p-type at a concentration of 5 × 1018 cm−3.

For the cases with p-type doping concentration of 5 × 1018 cm−3, only the ML and 2L cases show a very small barrier height ({varPhi}_{p}) (0.13 eV for ML and 0.05 eV for 2L). For the 3L and 4L cases, there is zero barrier height. ({varPhi}_{n}) is 1.35 eV for ML and 1.18 eV for 2–4L, as shown in Table 1. For the cases with p-type doping concentration of 5 × 1018 cm−3, the bandgap shrinks to 1.48 eV for ML TiS2 and 1.18 eV for 2–4L.

As inferred from Fig. 5d, when the doping is p-type with a concentration of 5 × 1018 cm−3, the contact is ohmic for p-type carriers while the barrier for n-type carriers is still large. As mentioned earlier, the doping concentration (P_{mathrm{c}}) was added to the ML MoS2 within the contact region ranges from 3.85 × 1017 to 2.63 × 1018 cm−3. When the p-type doping of channel MoS2 reaches the value of (P_{mathrm{c}}), the band will become flat, and the contact becomes an ohmic contact. Thus, TiS2 can be used as an either an ohmic or Schottky contact depending on the doping of the ML MoS2.