  We assess the impact of the scattering physics assumptions on the
thermoelectric properties of five Co-based p-type half-Heusler alloys by
considering full energy-dependent scattering times, versus the commonly
employed constant scattering time. For this, we employ DFT bandstructures and a
full numerical scheme that uses Fermi's Golden Rule to extract the momentum
relaxation times of each state at every energy, momentum, and band. We consider
electron-phonon scattering (acoustic and optical), as well as ionized impurity
scattering, and evaluate the qualitative and quantitative differences in the
power factors of the materials compared to the case where the constant
scattering time is employed. We show that the thermoelectric power factors
extracted from the two different methods differ in terms of i) their ranking
between materials, ii) the carrier density where the peak power factor appears,
and iii) their trends with temperature. We further show that the constant
relaxation time approximation smoothens out the richness in the bandstructure
features, thus limiting the possibilities of exploring this richness for
material design and optimization. These details are more properly captured
under full energy/momentum-dependent scattering time considerations. Finally,
by mapping the conductivities extracted within the two schemes, we provide
appropriate density-dependent constant relaxation times that could be employed
as a fast first order approximation for extracting charge transport properties
in the half-Heuslers we consider.
