Calculation of Defect Concentrations and Phase Stability in Cu$_2$ ZnSnS$_4$ and Cu$_2$ ZnSnSe$_4$ From Stoichiometry

The application of the quarternary compounds Cu
₂
ZnSnS
₄
(CZTS) and Cu
₂
ZnSnSe
₄
(CZTSe) as efficient solar cell absorber materials is dependent on the complex behavior of the large variety of intrinsic lattice defects. In this paper, a canonical approach is presented and applied to calculate the defect concentrations and the position of the Fermi level for CZTS and CZTSe at a given temperature as a function of stoichiometry (or a combination of stoichiometry and elemental chemical potentials). With the defect concentrations, the chemical potentials (which are generally not experimentally accessible) can be calculated, allowing the relation of sample composition to the phase stability of CZTS and CZTSe with respect to secondary compounds. Based on the model, it is shown that the stable CZTS with off-stoichiometric composition requires both Cu-poor and Zn-rich conditions, while the compositional space corresponding to stable CZTSe is wider than for CZTS. Additionally, the determination of the Fermi level directly relates the desired p-type conductivity to phase stability in both materials. The method used in this study is applicable to a wide range of complex materials.