  Vertical stacks of two-dimensional (2D) materials, separated by the van der
Waals gap and held together by the van der Waals forces, are immensely
promising for a plethora of nanotechnological applications. Charge control in
these stacks may be modeled using either a simple electrostatics approach or a
detailed atomistic one. In this paper, we compare these approaches for a gated
2D transition metal dichalcogenide bilayer and show that recently reported
electrostatics-based models of this system give large errors in band energy
compared to atomistic (Density Functional Theory) simulations. These errors are
due to the tails of the ionic potentials that reduce the electrical-equivalent
van der Waals gap between the 2D layers, and can be corrected by using the
reduced 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 2D
bilayer, the electrical-equivalent gap is less than 1 $\mathrm{\AA}$. For the
example of band-to-band tunneling based ultra low-power transistors, this is
seen to lead to errors of several hundred millivolts and more in the threshold
voltage estimated from electrostatics.
