# First-Principles Study of the Contact Resistance at 2D Metal/2D Semiconductor Heterojunctions
## 3 Structural and Electronic Properties of Graphene and MoS\({}_{2}\)  
Before discussing the contact resistance at 2D metal/semiconductor interfaces, we briefly present the structural and electronic properties of graphene and MoS\({}_{2}\). Graphene consists of a single (flat) layer of carbon atoms, arranged in a hexagonal network, as shown in Figure 3a [41; 42; 43; 44]. The C atoms are \(sp^{2}\)-hybridized in graphene, forming two single bonds (\(\sigma\)) and one double bond (\(\sigma\) and \(\pi\)) with their first neighbors. The computed lattice parameter of graphene, using DFT-GGA simulations, is about 2.47 A [3], typically 0.4% larger than the experimental one, i.e., 2.46 A [43; 44].  
The computed electronic band structure of graphene is shown in Figure 3b. The characteristic linear energy dispersion near the Fermi level is clearly observed, forming a so-called Dirac cone; the valence band (corresponding to \(\pi\) orbitals) and the conduction band (corresponding to \(\pi\) * orbitals) touch at the Fermi level E\({}_{\text{F}}\), resulting in a zero density of states at E\({}_{\text{F}}\). For this reason, graphene is often called a zero density-of-states metal or a zero band-gap semiconductor. Due to the linear energy band dispersion near the Fermi level, the electrons in graphene are considered as \"massless relativistic particles\". This peculiar property results in very high charge carrier mobilities in graphene, in the range of 10\({}^{4}\)-10\({}^{6}\) cm\({}^{2}\)/Vs [45; 46; 47].  
MoS\({}_{2}\) is a member of the transition metal dichalcogenide family. Monolayer and few-layer MoS\({}_{2}\) were investigated recently for their potential use in 2D material-based field-effect transistors and photonic devices [48; 49; 50; 51]. Each molybdenum atom is bonded to six sulfur atoms in MoS\({}_{2}\), with three S  
Figure 3: **(a)** Top view of the atomic configuration of graphene. **(b)** Computed electronic band structure of graphene. The Fermi level corresponds to the reference (zero energy) level.  
Figure 2: **(a)** Computed current–voltage (I–V) characteristics of a 1T-MoS\({}_{2}\)/2H-MoS\({}_{2}\)/1T-MoS\({}_{2}\) heterostructure. The resistance R of the structure is extracted from a linear fit to the data (solid line), in the voltage range between 0.2 and 0.8 V. **(b)** Resistance (multiplied by the channel width W) of the same heterostructure, for three different 2H-MoS\({}_{2}\) channel lengths. The dashed line is a linear fit to the data.  
atoms above and three below, in a trigonal prismatic or octahedral structure, forming a three-layered atomic sheet [52] (see Figure 4a). In bulk MoS\({}_{2}\), these sheets are \"bonded\" via weak Van der Waals forces. In its most stable form, bulk MoS\({}_{2}\) crystallizes in the 2H (trigonal prismatic) phase, with a lattice parameter of 3.16 A; the computed lattice parameter, using DFT-GGA simulations, is about 3.17 A [3]. Bulk 2H-MoS\({}_{2}\) is an indirect semiconductor, with an energy band-gap of about 1.2 eV. The band-gap of MoS\({}_{2}\) increases when the number of layers decreases, becoming a direct band-gap semiconductor at the limit of a MoS\({}_{2}\) single layer [53; 54], with a computed DFT-GGA band-gap of about 1.8 eV [3], as shown in Figure 4b. Depending on the growth conditions and/or on the chemical treatment [17; 55], 2H-MoS\({}_{2}\) can be transformed to the meta-stable 1T-MoS\({}_{2}\) phase. This octahedral phase has a computed lattice parameter of 3.15 A, and it is metallic [3; 56; 57; 58], as shown in Figure 4c.