  This work, presents a study of lifetime of carriers due to intrinsic
scattering mechanisms $viz.$ electron-electron (EEI), electron-phonon (EPI) and
phonon-phonon interactions (PPI) in a promising half-Heusler thermoelectric
FeVSb. Using the full-$GW$ method, the effect of EEI and temperature on the
valence and conduction band extrema and band gap are studied. The lifetime of
carriers with temperature are estimated at these band extrema. At 300 K,
estimated value of lifetime at VBM (CBM) is $\sim$1.91 x10$^{-14}s$ ($\sim$2.05
x10$^{-14}s$). The estimated ground state band gap considering EEI is $\sim$378
meV. Next, the effect of EPI on the lifetime of electrons and phonons with
temperature are discussed. The comparison of two electron lifetimes suggests
that EEI should be considered in transport calculations along with EPI. The
average acoustic, optical and overall phonon lifetimes due to EPI are studied
with temperature. Further, the effect of PPI is studied by computing average
phonon lifetime for acoustic and optical phonon branches. The lifetime of the
acoustic phonons are higher compared to optical phonons which indicates
acoustic phonons contribute more to lattice thermal conductivity
($\kappa_{ph}$). The comparison of phonon lifetime due to EPI and PPI suggests
that, above 500 K EPI is the dominant phonon scattering mechanism and cannot be
ignored in $\kappa_{ph}$ calculations. Lastly, a prediction of the power factor
and figure of merit of n-type and p-type FeVSb is made by considering the
temperature dependent carrier lifetime for the electronic transport terms. This
study shows the importance of considering EEI in electronic transport
calculations and EPI in phonon transport calculations. Our study is expected to
provide results to further explore the thermoelectric transport in this
material.
