Image-force barrier lowering in top- and side-contacted two-dimensional materials

We compare the image-force barrier lowering (IFBL) and calculate the resulting contact resistance for four different metal–dielectric-two-dimensional (2D) material configurations. We analyze edge contacts in three different geometries (a homogeneous dielectric throughout, including the 2D layer; a homogeneous dielectric surrounding the 2D layer, both ungated and back gated) and also a top-contact assuming a homogeneous dielectric. The image potential energy of each configuration is determined and added to the Schottky energy barrier which is calculated assuming a textbook Schottky potential. For each configuration, the contact resistivity is calculated using the WKB approximation and the effective mass approximation using either SiO2 or HfO2 as the surrounding dielectric. We obtain the lowest contact resistance of 1 kΩμm by n-type doping an edge contacted transition metal-dichalcogenide (TMD) monolayer, sandwiched between SiO2 dielectric, with ∼1012 cm−2 donor atoms. When this optimal configuration is used, the contact resistance is lowered by a factor of 50 compared to the situation when the IFBL is not considered.