Nonlocal Electrostatic Origin of Schottky-Barrier Variability in 2D Contacts

Abstract

Electrical contacts often limit the performance of atomically thin semiconductor devices. The Schottky barrier height (SBH) is conventionally treated as a local interface property, yet reported values for the same metal/2D-semiconductor contact vary by hundreds of meV. Here we show that, in top contacts, the effective SBH exhibits a pronounced nonlocal electrostatic dependence on defects near the contact edge, beyond the conventional local interface framework. A nonlocal electrostatic model, supported by density-functional-theory-based transport calculations for Ti--MoS$_2$ and Au--MoS$_2$, captures the large, metal-dependent variations in SBH as a function of defect position relative to the contact edge. These results provide a unified explanation for the longstanding variability in experimentally extracted SBHs and establish nonlocal electrostatics, mediated by edge-proximal defects, as a key mechanism governing carrier injection in 2D contacts.