Gate- versus defect-induced voltage drop and negative differential resistance in vertical graphene heterostructures

Vertically stacked two-dimensional (2D) van der Waals (vdW) heterostructures based on graphene electrodes represent a promising architecture for next-generation electronic devices. However, their first-principles characterizations have been so far mostly limited to the equilibrium state due limitation of standard non-equilibrium Green's function approach. To overcome these challenges, we introduce calculation method recently developed multi-space constrained-search density functional formalism and apply it graphene/few-layer hexagonal boron nitride (hBN)/graphene field-effect transistors. Our explicit finite-voltage calculations show that previously reported negative differential resistance (NDR) current-bias voltage characteristics can be produced not only from gating-induced mismatch between two Dirac cones but bias-dependent energetic shift defect levels. Specifically, carbon atom substituted nitrogen (C$_N$) within inner hBN layers, increase bias is found induce self-consistent electron filling in-gap C$_N$ states, which leads changes in drop profiles symmetric NDR characteristics. On other hand, with placed outer interfacial find pinning levels nearby states become bias-independent peaks disappear. Revealing hitherto undiscussed behaviors atomic critical impact device characteristics, our work points towards future directions computational design 2D vdW devices