# First-Principles Study of the Contact Resistance at 2D Metal/2D Semiconductor Heterojunctions
## 4 Graphene/2H-MoS\({}_{2}\) Edge Contacts  
We considered four different graphene/monolayer 2H-MoS\({}_{2}\) slab models, with various edge contact symmetries and/or terminations, as shown in Figure 5[59]. Large supercells (with about 250 atoms) were used for the DFT simulations, to minimize the strain in the graphene and MoS\({}_{2}\) layers (which is typically below 1.5% in both materials). The zigzag and armchair interface models were built by using (36.5 \(\times\) 19.4) A\({}^{2}\) and (36.8 \(\times\) 16.8) A\({}^{2}\) rectangular supercells, respectively. A vacuum layer of about 20 A was considered for each interface models, to avoid spurious interactions between adjacent cells. Model 1 was based on an armchair-edge interface, with a single graphene layer. After  
Figure 4: (a) Schematic representations of 2H, 3R, and 1T phases of transition metal dichalcogenides. (b) Computed electronic band structure of a 2H-MoS\({}_{2}\) monolayer. The reference energy level corresponds to the valence band edge. (c) Computed electronic band structure of a 1T-MoS\({}_{2}\) monolayer. The reference energy level corresponds to the Fermi level. relaxation, carbon-sulfur (2.14 A average bond length) and carbon-molybdenum (1.83 A average bond length) bonds were present at this interface, as well as sulfur dangling bonds (from the bottom sulfur sublayer). A graphene bilayer was considered in model 2, in order to saturate these dangling bonds by the formation of C-S bonds. Model 3 was based on a zigzag-edge interface, terminated by Mo atoms, where C-Mo bonds (2.13 A average bond length) were only present after relaxation, resulting in a \"defect-free\" contact model. A sulfur-terminated zigzag edge contact was considered in Model 4. In this case, only C-S bonds (1.79 A average bond length) were formed, but S dangling bonds were present in the bottom sulfur sublayer. The formation energy \(\gamma\) of the graphene/MoS\({}_{2}\) interface is calculated using the following equation [24; 60]:  
\[\gamma=\frac{1}{2\text{L}}\Big{(}\text{E}_{\text{total}}-\text{n}_{\text{C}} \text{n}_{\text{C}}-\text{n}_{\text{MO}}\text{u}_{\text{MoS}_{2}}-\text{\Delta n }_{\text{S}}\text{u}_{\text{S}}\Big{)}, \tag{3}\]  
where L is the interface length, E\({}_{\text{total}}\) is the total energy of the graphene/MoS\({}_{2}\)/graphene system, n\({}_{\text{i}}\) and u\({}_{\text{i}}\) are the number of atoms and their chemical potentials, respectively, u\({}_{\text{MoS}2}\) is the total energy of a MoS\({}_{2}\) (single layer) unit cell, and \(\text{\Delta n}_{\text{S}}=\text{n}_{\text{S}}-2\text{n}_{\text{Mo}}\). The chemical potential u\({}_{\text{Mo}}\) was fixed to that of body-centered cubic Mo, while u\({}_{\text{S}}=\frac{1}{2}\) (u\({}_{\text{Mo}\text{S}2}-\text{u}_{\text{Mo}}\)) in the Mo-rich limit, and u\({}_{\text{S}}=\text{u}_{\text{S(bulk)}}\) in the S-rich limit, where u\({}_{\text{S(bulk)}}\) corresponds to the sulfur chemical potential of a S\({}_{\text{S}}\) ring [24]. The computed interface formation energies of the slab models are shown in Table 1. The Mo-terminated zigzag interface model (model 3 in Figure 5) was the most stable one, in the molybdenum-rich limit. On the other hand, the armchair interface model, with a bilayer graphene layer, had the lowest \(\gamma\) in the sulfur-rich limit. Note that the Mo and S-terminated zigzag edge contacts,  
Figure 5: Top and side views of the relaxed atomic configurations of lateral graphene/MoS\({}_{2}\) interface models [59]. Model 1 and model 2 correspond to armchair edge contacts, with a single graphene layer and a double graphene layer, respectively. Models 3 and 4 correspond to zigzag edge contacts with Mo termination and S termination, respectively. Dark-gray, blue, and yellow spheres correspond to C, Mo, and S atoms, respectively. The S dangling bonds in model 1 and model 4 are encircled in red. with a graphene monolayer (model 3 and 4), also had comparable interface formation energies in the S-rich limit, with both interfaces likely produced during such a growth process.