Contacts to Two-dimensional Materials: Image Forces, Dielectric Environment, and Back-gate

We calculate the resistivity in back-gated metal-transition metal dichalcogenide (TMD) edge contacts in which the carrier injection is governed by the Schottky barrier at the interface. We keep the channel undoped and change the back-gate bias to electrostatically dope the channel. We use the electrostatic potential obtained from the numerical solution of the Poisson equation. We calculate the transmission coefficient within the Wentzel–Kramers–Brillouin (WKB) approximation and use the band structure from density functional theory (DFT). We obtain the effect of the image force analytically using the Green’s function for the Poisson equation with boundary conditions appropriate to the geometry we have considered. We find that a low-κ bottom oxide (gateoxide) in conjunction with low-κ top oxide results in a better contact resistance. We also find that impuritydoping the TMD layer results in a lower contact resistance than electrostatically doping it by a back-gate bias.