First-principles calculation of defect formation energy in chalcopyrite-type CuInSe2, CuGaSe2 and CuAlSe2

In order to quantitatively evaluate the formation energies of Cu, In/Ga/Al and Se vacancies in chalcopyrite-type CuInSe₂ (CIS), CuGaSe₂ (CGS) and CuAlSe₂ (CAS), first-principles pseudopotential calculations using plane-wave basis functions were performed. All calculations were performed using a supercell with 64 atoms, which was eight times greater than the number of atoms in a primitive cell with eight atoms. The formation energies of point defects were calculated as a function of the atomic chemical potentials of constituent elements. Atomic arrangements around the vacancy were optimized allowing relaxation of the first- and second-nearest-neighbor atoms of the vacancy. The obtained results were as follows: (1) the formation energy of Cu vacancy was smaller than those of the other vacancies in CIS, CGS and CAS. Under the Cu-poor condition, the formation energy of Cu vacancy in CIS was lowest among those in them; (2) the formation energy of Se vacancy in CIS was relatively lower than those in CGS and CAS; (3) the formation energy of (2V_Cu+In_Cu) pair in CIS was greatly dependent on the chemical potential of the constituent elements, i.e. Cu, In and Se. On the other hand, the formation energies of (2V_Cu+Ga_Cu) in CGS and (2V_Cu+Al_Cu) in CAS were not largely dependent on the chemical potential of the constituent elements. Under the Cu-poor condition, the formation energy of (2V_Cu+In_Cu) pair in CIS was much lower than those of (2V_Cu+Ga_Cu) in CGS and (2V_Cu+Al_Cu) in CAS.