  Photoluminescence spectra, shows that monolayer Transition-metal
dichalcogenides (MLTMDCs), possess charged exciton binding energies,
conspicuously similar to the energy of optical phonons. This enigmatic
coincidence has offered opportunities to investigate many-body interactions
between trion, exciton and phonon and led to efficient excitonic anti-Stokes
processes with the potential for laser refrigeration and energy harvesting. In
this study, we show that in WSe2 materials, the trion binding energy matches
two phonon modes, the outofplane HP and the in-plane LO mode. In this respect,
using the Fermi golden rule together with the effective mass approximation, we
investigate the rate of the population transfers between exciton and trion,
mediated by a single phonon. We demonstrate that, while the absolute importance
of the two phonon modes on the upconversion process strongly depend on the
experimental conditions such as the temperature and the dielectric environment
(substrate), both modes lead to an up-conversion process on time scales in the
range of few picoseconds to sub-nanosecond, consistent with recents
experimental findings. The conjugate process is also investigated in our study,
as a function of temperature and electron density . We prove that exciton to
trion down-conversion process is very unlikely at low electron density and high
temperature while it increases dramatically to reach few picoseconds time scale
at low temperature and for electron density . Finally, our results show that
conversion process occurs more rapidly in exemplary monolayer molybdenum-based
dichalcogenides (MoSe2 and MoTe2) than tungsten dichalcogenides .
