Image-force barrier lowering of Schottky barriers in two-dimensional materials as a function of metal contact angle

Two-dimensional (2D) semiconductors are a promising solution for the miniaturization of electronic devices and for the exploration of novel physics. However, practical applications and demonstrations of physical phenomena are hindered by high Schottky barriers at the contacts to 2D semiconductors. While the process of image-force barrier lowering (IFBL) can considerably decrease the Schottky barrier, IFBL is not fully understood for the majority of prevalent contact geometries. We introduce an alternative technique to determine the IFBL potential energy with application spanning far beyond that of any existing method. We do so by solving Poisson's equation with the boundary conditions of two metal surfaces separated by an angle $\mathrm{\ensuremath{\Omega}}$. We then prove that our result can also be obtained with the method of images provided a non-Euclidean, cone manifold space is used. The resulting IFBL is used to calculate the expected contact resistance of the most prevalent contact geometries. Finally, we investigate contact resistance and show how stronger IFBL counteracts the effect of larger depletion width with increasing contact angle. We find that top contacts experience lower contact resistance than edge contacts. Remarkably, our results identify tunable parameters for reducing Schottky barriers and likewise contact resistance to edge-contacted 2D materials, enhancing potential applications.