Stability and Electronic Structure of $Cu_{2} ZnSnS_{4} $ Surfaces: a First-Principles Study

Through the surface energy first-principles calculations, we studied the possible surface structures of the frequently observed cation-terminated (112) and anion-terminated ($\overline {112} )$ surfaces in various sample grown conditions. We found that the polar surfaces are stabilized by the charge-compensating defects, such as vacancies ($V_{Cu} $,$V_{Zn} )$, antisites ($Zn_{Cu} $,$Zn_{Sn} $ , $Sn_{Zn} )$ and defect clusters ($Cu_{Zn} +Cu_{Sn} $,$2Zn_{Cu} +V_{Sn} $ ). In stoichiometric single-phase CZTS samples, Cu-enriched defects are favored on (112) surfaces and Cu--depleted defects are favored on ($\overline {112}$) surfaces, while in non-stoichiometric samples grown under Cu poor and Zn rich conditions, both surfaces favor the Cu-depleted defects, which explains the observed Cu-deficiency on the surfaces of the synthesized CZTS thin films. The electronic structure analysis shows that Cu-enriched surfaces produce detrimental states in the band gap, while Cu-depleted surfaces produce no gap states and are thus benign to the solar cell performance. The calculated surface properties are consistent with experimental observation that Cu-poor and Zn-rich CZTS solar cells have higher efficiency.