Image force derivation and application to two-dimensional materials contacts

Transistors made from two-dimensional (2D) materials such as transition-metal dichalcogenides (TMDs) are characterized by high contact resistances. To make performant devices, it is important to estimate the contact resistances accurately using suitable models.

Most models do not include the image-force barrier lowering (IFBL) that arises due to electrons in the TMD being attracted to the image charge in the metal. We derive an analytical expression for the IFBL of metal wedges of angle $Omega$ using the Kontorovich-Lebedev transform to expand the solutions of the Poisson equation in cylindrical coordinates. We show that the IFBL can also be calculated using the method of images by mapping the wedge geometry to a parallel plate using a conifold geometry. We find that for large opening angle $Omega$, the electric field lines due to metal surface charge are spread out more compared to smaller opening angles leading to less IFBL at large opening angles.

We develop a semi-classical transport model based on the Bardeen transfer method to calculate the contact resistance in top contacts adding the IFBL to the depletion potential arising from the Schottky contact. We calculate and compare the contact resistance with and without the IFBL. We find that including the IFBL improves the contact resistance up to 30 times at n-type doping of $sim 10^{11}$ cm$^{-2}$.