First-principles calculations of vacancy formation in In-free photovoltaic semiconductor Cu2ZnSnSe4

To quantitatively evaluate the formation energies of Cu, Zn, Sn, and Se vacancies in kesterite-type Cu2ZnSnSe4 (CZTSe), first-principles pseudopotential calculations using plane-wave basis functions were performed. The formation energies of neutral Cu, Zn, Sn and Se vacancies were calculated as a function of the atomic chemical potentials of constituent elements. The obtained results were as follows: (1) the formation energy of Cu vacancy was generally smaller than those of the other Zn, Sn and Se vacancies, (2) under the Cu-poor and Zn-rich condition, the formation energy of Cu vacancy was particularly low, (3) the formation energy of Zn vacancy greatly depended on the chemical potentials of the constituent elements and under the Zn-poor and Se-rich condition, the formation energy of Zn vacancy was smaller than that of Cu vacancy, and (4) the formation energy of Sn vacancy did not greatly depend on the chemical potentials of the constituent elements and was much larger than those of Cu, Zn, and Se vacancies. These results indicate that Cu vacancy is easily formed under Cu-poor and Zn-rich conditions, but Zn vacancy is easily formed under the Zn-poor and Se-rich conditions.