  Accurately described excitonic properties of transition metal dichalcogenide
heterobilayers (HBLs) are crucial to comprehend the optical response and the
charge carrier dynamics of them. Excitons in multilayer systems posses inter or
intralayer character whose spectral positions depend on their binding energy
and the band alignment of the constituent single-layers. In this study, we
report the electronic structure and the absorption spectra of MoS$_2$/WS$_2$
and MoSe$_2$/WSe$_2$ HBLs from first-principles calculations. We explore the
spectral positions, binding energies and the origins of inter and intralayer
excitons and compare our results with experimental observations. The absorption
spectra of the systems are obtained by solving the Bethe-Salpeter equation on
top of a G$_0$W$_0$ calculation which corrects the independent particle
eigenvalues obtained from density functional theory calculations. Our
calculations reveal that the lowest energy exciton in both HBLs possesses
interlayer character which is decisive regarding their possible device
applications. Due to the spatially separated nature of the charge carriers, the
binding energy of inter-layer excitons might be expected to be considerably
smaller than that of intra-layer ones. However, according to our calculations
the binding energy of lowest energy interlayer excitons is only $\sim$ 20\%
lower due to the weaker screening of the Coulomb interaction between layers of
the HBLs. Therefore, it can be deduced that the spectral positions of the
interlayer excitons with respect to intralayer ones are mostly determined by
the band offset of the constituent single-layers. By comparing oscillator
strengths and thermal occupation factors, we show that in luminescence at low
temperature, the interlayer exciton peak becomes dominant, while in absorption
it is almost invisible.

Materials Science