Role of electrostatic doping on the resistance of metal and two-dimensional materials edge contacts

In this theoretical study, we compare electrostatically doped metal-transition metal dichalcogenide (TMD) edge-contacts versus substitutionally doped edge-contacts in terms of their contact resistance. Our approach involves the utilization of electrostatic doping achieved by applying back-gate bias to the metal-TMD edge contacts, where carrier injection is primarily governed by the Schottky barrier at the interface. To analyze these contacts, we employ the Wentzel-Kramers-Brillouin (WKB) approximation to calculate the transmission coefficient and use density functional theory (DFT)-derived band structures. We numerically solve the Poisson equation to capture the electrostatic potential. We also account for the impact of the image force using Green's function for the Poisson equation with boundary conditions appropriate to our specific geometry. Our findings reveal that electrostatically doped TMD edge contacts exhibit higher contact resistance compared to impurity-doped edge contacts at equivalent carrier concentrations. At the same time, we find that, among the electrostatically doped edge contacts, a low-$\kappa$ back-gate oxide in conjunction with low-$\kappa$ top oxide is preferable in terms of improvement in contact resistance. For instance, in a metal-TMD edge contact scenario involving a monolayer ${\mathrm{MoS}}_2$ as the channel, ${\mathrm{SiO}}_2$ as the infinitely thick top oxide, and a ${\mathrm{SiO}}_2$ back-gate oxide with an equivalent oxide thickness (EOT) of $1\mathrm{nm}$, we demonstrate that it is possible to achieve an impressively low contact resistance of $50\mathrm{\Omega }\mu \mathrm{m}$ when the back-gate bias exceeds or equals 2 V.