  Electronic and transport properties of CuGaTe$_2$, a hole-doped ternary
copper based chalcopyrite type semiconductor, are studied using calculations
within the Density Functional Theory and solving the Boltzmann transport
equation within the constant relaxation time approximation. The electronic
bandstructures are calculated by means of the full-potential linear augmented
plane wave method, using the Tran-Blaha modified Becke-Johnson potential. The
calculated band gap of 1.23 eV is in agreement with the experimental value of
1.2 eV. The carrier concentration- and temperature dependent thermoelectric
properties of CuGaTe$_2$ are derived, and a figure of merit of $zT= 1.69$ is
obtained at 950 K for a hole concentration of $3.7\cdot10^{19}$ cm$^{-3}$, in
agreement with a recent experimental finding of $zT= 1.4$, confirming that
CuGaTe$_2$ is a promising material for high temperature thermoelectric
applications. The good thermoelectric performance of p-type CuGaTe$_2$ is
associated with anisotropic transport from a combination of heavy and light
bands. Also for CuSbS$_2$ (chalcostibite) a better performance is obtained for
p-type than for n-type doping. The variation of the thermopower as a function
of temperature and concentration suggests that CuSbS$_2$ will be a good
thermoelectric material at low temperatures, similarly to the isostructural
CuBiS$_2$ compound.
