  Density functional theory calculations are used to show that it is possible
to dope semiconducting transition metal dichalcogenides (TMD) such as MoS$_2$
and WS$_2$ with electrons and/or holes either by chemical substitution or by
adsorption on the sulfur layer. Notably, the activation energies of Lithium and
Phosphorus, a shallow donor and a shallow acceptor, respectively, are smaller
than 0.1 eV. Substitutional halogens are also proposed as alternative donors
adequate for different temperature regimes. All dopants proposed result in very
little lattice relaxation and, hence, are expected to lead to minor scattering
of the charge carriers. Doped MoS$_2$ and WS$_2$ monolayers are extrinsic in a
much wider temperature range than 3D semiconductors, making them superior for
high temperature electronic and optoelectronic applications.
