  Doping via electrostatic gating is a powerful and widely used technique to
tune the electron densities in layered materials. The microscopic details of
how these setups affect the layered material are, however, subtle and call for
careful theoretical treatments. Using semiconducting monolayers of transition
metal dichalcogenides (TMDs) as prototypical systems affected by electrostatic
gating, we show that the electronic and optical properties change indeed
dramatically when the gating geometry is properly taken into account. This
effect is implemented by a self-consistent calculation of the Coulomb
interaction between the charges in different sub-layers within the
tight-binding approximation. Thereby we consider both, single- and double-sided
gating. Our results show that, at low doping levels of $10^{13}$ cm$^{-2}$, the
electronic bands of monolayer TMDs shift rigidly for both types of gating, and
subsequently undergo a Lifshitz transition. When approaching the doping level
of $10^{14}$ cm$^{-2}$, the band structure changes dramatically, especially in
the case of single-sided gating where we find that monolayer \ce{MoS2} and
\ce{WS2} become indirect gap semiconductors. The optical conductivities
calculated within linear response theory also show clear signatures of these
doping-induced band structure renormalizations. Our numerical results based on
light-weighted tight-binding models indicate the importance of electronic
screening in doped layered structures, and pave the way for further
understanding gated super-lattice structures formed by mutlilayers with
extended Moir\'{e} pattern.
