  In the quest of new thermoelectric (TE) materials with high power factors,
full-Heusler compounds having flat band are found to be promising candidates.
In this direction, Fe$_{2}$ScX (X=P,As,Sb) compounds are investigated using mBJ
for the band gap and SCAN to describe the electronic bands and phonon
properties for TE applications. The band gaps obtained from mBJ are 0.81 eV,
0.69 eV and 0.60 eV for Fe$_{2}$ScX compounds, respectively. The phonon
dispersion, phonon density of states (DOS) and partial DOS are calculated. The
phonon contributions to specific heat are obtained as a function of temperature
under harmonic approximation. The electronic band structutre calculated from
mBJ and SCAN functionals are qualitatively compared. The TE parameters are
calculated for both hole and electron dopings under semiclassical theory. We
use simple, but reasonable method to estimate phonon relaxation time
($\tau_{ph}$). Using the specific heat, estimated $\tau_{ph}$ and slopes (phase
velocity) of acoustic branches in the linear region, lattice thermal
conductivity ($\kappa_{ph}$) at 300 K is calculated for three compounds. The
obtained values of $\kappa_{ph}$ with constant $\tau_{ph}$ are 18.2, 13.6 and
10.3 $Wm^{-1}K^{-1}$, respectively. Finally, the temperature dependent figure
of merit $ZT$ values are calculated for optimal carrier concentrations in the
doping range considered, to evaluate the materials for TE application. The $ZT$
values for n-type Fe$_{2}$ScX, in 900-1200 K, are 0.34-0.43, 0.40-0.48 and
0.45-0.52, respectively. While, the p-type Fe$_{2}$ScX have $ZT$ of 0.25-0.34,
0.20-0.28 and 0.18-0.26, respectively in the same temperature range. The $ZT$
values suggest that, Fe$_{2}$ScX compounds can be promising materials in high
temperature power generation application on successful synthesis and further
$\kappa_{ph}$ reduction by methods like nanostructuring.
