Wurtzite-derived polytypes of kesterite and stannite quaternary chalcogenide semiconductors

The ${\text{I}}_{2}{\text{-II-IV-VI}}_{4}$ quaternary chalcogenide semiconductors (e.g., ${\text{Cu}}_{2}{\text{ZnGeS}}_{4}$, ${\text{Cu}}_{2}{\text{ZnSnS}}_{4}$, ${\text{Cu}}_{2}{\text{ZnGeSe}}_{4}$ ${\text{Cu}}_{2}{\text{CdSnSe}}_{4}$, and ${\text{Ag}}_{2}{\text{CdGeSe}}_{4}$) have been studied for more than 40 years but the nature of their crystal structures has proved contentious. Literature reports exist for the stannite and kesterite mineral structures, which are zinc-blende-derived structures, and wurtzite-stannite, which is a wurtzite-derived structure. In this paper, through a global search based on the valence octet rule (local charge neutrality), we report a wurtzite-derived structure corresponding to the kesterite structure, namely, wurtzite-kesterite (space group $Pc$), which is the ground state for some ${\text{I}}_{2}{\text{-II-IV-VI}}_{4}$ compounds, but is easily confused with the wurtzite-stannite (space-group $Pmn{2}_{1}$) structure. We show that there is a clear relationship between the properties of the wurtzite-kesterite and zinc-blende-derived kesterite structures, as well as between wurtzite-stannite and stannite. Contributions from the strain and Coulomb energies are found to play an important role in determining the structural stability. The underlying trends can be explained according to the size and ionicity of the group-I, -II, -IV, and -VI atoms. Electronic-structure calculations show that the wurtzite-derived structures have properties similar to the zinc-blende-derived structures, but their band gaps are relatively larger, which has also been observed for binary II-VI semiconductors.