Image-Force Barrier Lowering for Two-Dimensional Materials: Direct Determination and Method of Images on a Cone Manifold

The future use of two-dimensional (2D) semiconducting materials for electronic device applications hinges on the ability to make low-resistance contacts. To model such contacts, an accurate expression of the image force barrier-lowering (IFBL) is needed. We derive the image-force energy by solving Poisson's equation with the boundary conditions of two metal surfaces separated by an angle omega. We show how the image-force energy can also be obtained using the method of images provided a non-Euclidian cone-manifold space is used. We calculate how much the IFBL is strengthened or weakened for various omega and angles with the 2D semiconductor. For the most prominent 2D material contact configuration, the image-force energy is reduced by a factor of 0.85, but a smaller angle between the metal surfaces can significantly increase the image-force energy. We predict that a contact with a small angle between the metal and 2D material and a surrounding dielectric with low permittivity will yield low contact resistance by enhancing IFBL.
Comment: 13 pages, 5 figures