# First-Principles Study of the Contact Resistance at 2D Metal/2D Semiconductor Heterojunctions
## 4 Graphene/2H-MoS\({}_{2}\) Edge Contacts
The computed \(\mathrm{R_{c}W}\) of the different edge-contact models is also shown in Table 1. The contact resistances for the \"defect-free\" interfaces (model 2 and 3) were typically between 220 and 560 \(\mathrm{\Omega\_{\mathrm{\mu}}m}\). These values are comparable to those reported at graphene/metal edge contacts [61]. On the other hand, the \(\mathrm{R_{c}W}\) at interfaces with sulfur dangling bonds was about two orders of magnitude larger. The transmission probabilities of the Mo and S terminated zigzag interface models are discussed below, in order to gain further insight into these results. The computed (zero-bias) transmission spectrum of the molybdenum-terminated zigzag interface model (model 3) is shown in Figure 6a. The onset of transmission is at about 0.1 eV from the Fermi level, a result which is in agreement with the energy barrier height \(\Phi_{\mathrm{B}}\) of about 0.1 eV, calculated from the electrostatic potential profile of the heterostructure [59], as well as from the graphene and MoS\({}_{2}\) contributions to the electronic density of states, shown in Figure 6b. Note that the computed graphene work function and MoS\({}_{2}\) electron affinity were about 4.4 eV and 4.2 eV, respectively, resulting in an \"ideal\" interface barrier of 0.2 eV. The barrier height at the Mo-terminated interface model was reduced by about 0.1 eV from the ideal value, due to the presence of polar C-Mo bonds (electrons transferred from Mo to C atoms), forming a dipole layer at the interface, as illustrated in Figure 7a. These C-Mo bonds significantly contributed to the electronic density of states near the Fermi level, as indicated from the isosurface charge density plot shown in the inset of Figure 6b. The resulting low energy barrier at the Mo-terminated zigzag interface led to a low \(\mathrm{R_{c}W}\), in the range of 200 \(\mathrm{\Omega\_{\mathrm{\mu}}m}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Interface Model**} & \(\boldsymbol{\gamma}\) **(eV/Å)** & \(\boldsymbol{\gamma}\) **(eV/Å)** & \multirow{2}{*}{**R\({}_{\mathrm{c}W}\) (\(\mathrm{\Omega\_{\mathrm{\mu}}m}\))**} \\  & **Mo-Rich Limit** & & \\ \hline Model 1 & 2.4 & 2.4 & \(8.1\times 10^{3}\) \\ Model 2 & 1.5 & 1.5 & \(5.6\times 10^{2}\) \\ Model 3 & 1.2 & 1.8 & \(2.2\times 10^{2}\) \\ Model 4 & 2.6 & 1.9 & \(2.3\times 10^{4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Computed interface formation energies \(\boldsymbol{\gamma}\) of the different graphene/MoS\({}_{2}\) interface models shown in Figure 5, in the Mo-rich and S-rich limit, respectively. The value of the computed contact resistance \(\mathrm{R_{c}W}\) of each interface model is also given. Figure 6: (**a**) Computed transmission spectrum (at zero bias) of a graphene/MoS\({}_{2}\) lateral heterostructure with Mo-terminated zigzag edge contacts (model 3 in Figure 5). The Fermi level corresponds to the reference (zero) energy. **(b**) Partial electronic density of states (PDOS) of graphene and MoS\({}_{2}\). The inset shows the isosurface charge density (0.01 e/Å\({}^{3}\)) near the Fermi level. Adapted from Reference [59]. The (zero-bias) transmission probability of the S-terminated zigzag interface model, with a large density of sulfur dangling bonds (model 4), is shown in Figure 8a. The onset of the transmission probability was at about 0.4 eV from the Fermi level at this interface, and the transmission was much reduced, in comparison to the molybdenum-terminated interface model. The energy barrier \(\Phi_{\text{B}}\), extracted from the electrostatic potential profile [59] and the partial electronic density of states, shown in Figure 8b, was increased by about 0.3 eV at the S-terminated contact, due to the presence of S dangling bonds, which produced gap states at about 0.4-0.5 eV below the MoS\({}_{2}\) conduction band.