Image-Force Barrier Lowering of Schottky Barriers in Two-Dimensional Materials as a Function of Metal Contact Angle

TL;DR

This paper introduces a novel method to analyze image-force barrier lowering in 2D semiconductor contacts, revealing how contact geometry influences contact resistance and offering strategies to reduce Schottky barriers for improved device performance.

Contribution

A new technique to calculate image-force barrier lowering in 2D contacts using Poisson's equation and non-Euclidean geometry, applicable to various contact geometries.

Findings

Top contacts have lower resistance than edge contacts.

Stronger image-force barrier lowering reduces contact resistance.

Contact angle significantly affects Schottky barrier height.

Abstract

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 a novel 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 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 geometric contacts. Finally, we investigate contact resistance and show how the 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.