  Cu$_3$SbSe$_4$ is a promising thermoelectric material due to high thermopower
($>400\ \mu$V/K) at 300K and higher. Although it has a simple crystal structure
derived from zinc blende structure, previous work has shown that the physics of
band gap formation is quite subtle due to the importance of active lone pair
(5$s^2$) of Sb and the non-local exchange interaction between these and Se 5$p$
electrons. Since for any application of semiconductors understanding the
properties of defects is essential, we discuss the results of a systematic
study of several point defects in Cu$_3$SbSe$_4$ including vacancies and
substitutions for each of the components. First principles calculations using
density functional theory show that among variety of possible dopants, $p$-type
doping can be done by substituting Sb with group $IV$ elements including Sn,
Ge, Pb and Ti and $n$-type doping can be done by replacing Cu by Mg, Zn. Doping
at the Se site appears to be rather difficult. Electronic structure
calculations also suggest that the $p$-type behavior seen in nominally pure
Cu$_3$SbSe$_4$ is most likely due to Cu vacancy rather than Se vacancy.
