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Vertically stacked two-dimensional (2D) van der Waals (vdW) heterostructuresbased on graphene electrodes represent a promising architecture fornext-generation electronic devices. However, their first-principlescharacterizations have been so far mostly limited to the equilibrium state dueto the limitation of the standard non-equilibrium Green's function approach. Toovercome these challenges, we introduce a non-equilibrium first-principlescalculation method based on the recently developed multi-spaceconstrained-search density functional formalism and apply it tographene/few-layer hexagonal boron nitride (hBN)/graphene field-effecttransistors. Our explicit finite-voltage first-principles calculations showthat the previously reported negative differential resistance (NDR)current-bias voltage characteristics can be produced not only from thegating-induced mismatch between two graphene Dirac cones but from thebias-dependent energetic shift of defect levels. Specifically, for a carbonatom substituted for a nitrogen atom (C$_N$) within inner hBN layers, theincrease of bias voltage is found to induce a self-consistent electron fillingof in-gap C$_N$ states, which leads to changes in voltage drop profiles andsymmetric NDR characteristics. On the other hand, with a C$_N$ placed on outerinterfacial hBN layers, we find that due to the pinning of C$_N$ levels tonearby graphene states voltage drop profiles become bias-independent and NDRpeaks disappear. Revealing hitherto undiscussed non-equilibrium behaviors ofatomic defect states and their critical impact on device characteristics, ourwork points towards future directions for the computational design of 2D vdWdevices

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