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.
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