  The quasiparticle spectra of atomically thin semiconducting transition metal
dichalcogenides (TMDCs) and their response to an ultrafast optical excitation
critically depend on interactions with the underlying substrate. Here, we
present a comparative time- and angle-resolved photoemission spectroscopy
(TR-ARPES) study of the transient electronic structure and ultrafast carrier
dynamics in the single- and bilayer TMDCs MoS$_2$ and WS$_2$ on three different
substrates: Au(111), Ag(111) and graphene/SiC. The photoexcited quasiparticle
bandgaps are observed to vary over the range of 1.9-2.3 eV between our systems.
The transient conduction band signals decay on a sub-100 fs timescale on the
metals, signifying an efficient removal of photoinduced carriers into the bulk
metallic states. On graphene, we instead observe two timescales on the order of
200 fs and 50 ps, respectively, for the conduction band decay in MoS$_2$. These
multiple timescales are explained by Auger recombination involving MoS$_2$ and
in-gap defect states. In bilayer TMDCs on metals we observe a complex
redistribution of excited holes along the valence band that is substantially
affected by interactions with the continuum of bulk metallic states.
