  We study the conduction band spin splitting that arises in transition metal
dichalcogenide (TMD) semiconductor monolayers such as MoS$_2$, MoSe$_2$, WS$_2$
and WSe$_2$ due to the combination of spin-orbit coupling and lack of inversion
symmetry. Two types of calculation are done. First, density functional theory
(DFT) calculations based on plane waves and pseudo potentials that yield large
splittings, between 3 and 30 meV. Second, we derive a tight-binding model, that
permits to address the atomic origin of the splitting. The basis set of the
model is provided by the maximally localized Wannier orbitals, obtained from
the DFT calculation, and formed by 11 atomic-like orbitals corresponding to
5$d$ and 3$p$ orbitals of the transition metal (W,Mo) and chalcogenide (S,Se)
atoms respectively. In the resulting Hamiltonian we can independently change
the atomic spin-orbit coupling constant of the two atomic species at the unit
cell, which permits to analyse their contribution to the spin splitting at the
high symmetry points. We find that ---in contrast to the valence band--- both
atoms give comparable contributions to the conduction band splittings. Given
that these materials are most often $n-$doped, our findings are important for
developments in TMD spintronics.
