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

Abstract

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 Ω. 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 Ω and angles with the 2D semiconductor. For the most prominent 2D material contact configuration, the image-force energy is reduced by a factor 6 − 2/ √ 3 ≈ 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.