  In-growth or post-deposition treatment of $Cu_{2}ZnSnS_{4}$ (CZTS) absorber
layer had led to improved photovoltaic efficiency, however, the underlying
physical mechanism of such improvements are less studied. In this study, the
thermodynamics of Na and K related defects in CZTS are investigated from first
principle approach using hybrid functional, with chemical potential of Na and K
established from various phases of their polysulphides. Both Na and K
predominantly substitute on Cu sites similar to their behavior in
$Cu(In,Ga)Se_{2}$, in contrast to previous results using the generalized
gradient approximation (GGA). All substitutional and interstitial defects are
shown to be either shallow levels or highly energetically unfavorable. Defect
complexing between Na and abundant intrinsic defects did not show possibility
of significant incorporation enhancement or introducing deep n-type levels. The
possible benefit of Na incorporation on enhancing photovoltaic efficiency is
discussed. The negligible defect solubility of K in CZTS also suggests possible
surfactant candidate.
