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

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-MoS2 and Au-MoS2, captures the large, metal-dependent variations in SBH as a function of defect position relative to the contact edge. These results identify edge-mediated nonlocal electrostatics as a mechanism that can contribute substantially to experimentally extracted SBH variability. We also show that edge-proximal perturbations can either raise or lower the barrier, providing testable routes for modifying carrier injection in 2D contacts.