  We investigate the interactions of photoexcited carriers with lattice
vibrations in thin films of the layered transition metal dichalcogenide (TMDC)
WSe$_2$. Employing femtosecond electron diffraction with monocrystalline
samples and first principle density functional theory calculations, we obtain a
momentum-resolved picture of the energy-transfer from excited electrons to
phonons. The measured momentum-dependent phonon population dynamics are
compared to first principle calculations of the phonon linewidth and can be
rationalized in terms of electronic phase-space arguments. The relaxation of
excited states in the conduction band is dominated by intervalley scattering
between $\Sigma$ valleys and the emission of zone-boundary phonons.
Transiently, the momentum-dependent electron-phonon coupling leads to a
non-thermal phonon distribution, which, on longer timescales, relaxes to a
thermal distribution via electron-phonon and phonon-phonon collisions. Our
results constitute a basis for monitoring and predicting out of equilibrium
electrical and thermal transport properties for nanoscale applications of
TMDCs.
