  Janus MoSSe monolayers were recently synthesised by replacing S by Se on one
side of MoS$_2$ (or vice versa for MoSe$_2$). Due to the different
electronegativity of S and Se these structures carry a finite out-of-plane
dipole moment. As we show here by means of density functional theory (DFT)
calculations, this intrinsic dipole leads to the formation of built-in electric
fields when the monolayers are stacked to form $N$-layer structures. For
sufficiently thin structures ($N<4$) the dipoles add up and shift the vacuum
level on the two sides of the film by $\sim N \cdot 0.7$ eV. However, for
thicker films charge transfer occurs between the outermost layers forming
atomically thin n- and p-doped electron gasses at the two surfaces. The doping
concentration can be tuned between about $5\cdot 10^{12}$ e/cm$^{2}$ and
$2\cdot 10^{13}$ e/cm$^{2}$ by varying the film thickness. The surface charges
counteract the static dipoles leading to saturation of the vacuum level shift
at around 2.2 eV for $N>4$. Based on band structure calculations and the
Mott-Wannier exciton model, we compute the energies of intra- and interlayer
excitons as a function of film thickness suggesting that the Janus multilayer
films are ideally suited for achieving ultrafast charge separation over atomic
length scales without chemical doping or applied electric fields. Finally, we
explore a number of other potentially synthesisable 2D Janus structures with
different band gaps and internal dipole moments. Our results open new
opportunities for ultrathin opto-electronic components such as tunnel diodes,
photo-detectors, or solar cells.
