  Transition metal dichalcogenides (TMDs) are promising candidates for a wide
variety of ultrascaled electronic, quantum computation, and optoelectronic
applications. The exponential decay of electronic density of states into the
bandgap, i.e. the band tail has a strong impact on the performance of TMD
applications. In this work, the band tails of various TMD monolayer and
multilayer systems when placed on various dielectric substrates is predicted
with density functional theory based nonequilibrium Green's functions. Nonlocal
scattering of electrons on polar optical phonons, charged impurities and remote
scattering on phonons in the dielectric materials is included in the
self-consistent Born approximation. The band tails are found to critically
depend on the layer thickness, temperature, doping concentration and
particularly on the chosen dielectric substrate. The underlying physical
mechanisms are studied in high detail and an analytical interpolation formula
is given to provide a quick-reference for Urbach parameters in $MoS_2$, $WS_2$
and $WSe_2$.
