  We investigate excitons in stacked transition metal dichalcogenide (TMDC)
layers under perpendicularly applied electric field, herein MoSe$_2$/WSe$_2$
van der Waals heterostructures. Band structures are obtained with density
functional theory calculations, along with the electron and hole wave functions
in conduction and valence bands, respectively. Although the type-II nature of
the heterostructure leads to fully charge separated inter-layer excitons,
charge carriers distribution among the layers is shown to be easily tunable by
external field. Our results show that moderate values of electric field produce
more evenly distributed wave functions along the heterostructure, thus
enhancing both the inter-layer exciton binding energy and, most notably, its
oscillator strength.
