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Vertical stacks of two-dimensional (2D) materials, separated by the van derWaals gap and held together by the van der Waals forces, are immenselypromising for a plethora of nanotechnological applications. Charge control inthese stacks may be modeled using either a simple electrostatics approach or adetailed atomistic one. In this paper, we compare these approaches for a gated2D transition metal dichalcogenide bilayer and show that recently reportedelectrostatics-based models of this system give large errors in band energycompared to atomistic (Density Functional Theory) simulations. These errors aredue to the tails of the ionic potentials that reduce the electrical-equivalentvan der Waals gap between the 2D layers, and can be corrected by using thereduced gap in the electrostatic model. For a physical van der Waals gap(defined as the chalcogen to chalcogen distance) of 3 $\mathrm{\AA}$ in a 2Dbilayer, the electrical-equivalent gap is less than 1 $\mathrm{\AA}$. For theexample of band-to-band tunneling based ultra low-power transistors, this isseen to lead to errors of several hundred millivolts and more in the thresholdvoltage estimated from electrostatics.

Electrical-equivalent van der Waals gap for 2D bilayers