Cation vacancies in the alloy compounds of Cu2ZnSn(S1-xSex)4 and CuIn(S1-xSex)2

The present work analyzes theoretically the formation energy of the cation vacancies V-Cu, V-In, V-Zn, and V-Sn in Cu2ZnSn(S1-xSex)(4) and CuIn(S1-xSex)(2) alloy compounds. An atomistic first-principles study is carried out by employing a generalized gradient approximation and a hybrid functional approach within the density functional theory, using the supercell approach to model the alloy compositions x = 0.00, 0.25, 0.50, 0.75, and 1.00. We find that the Cu vacancy is the most dominant cation vacancy with the lowest formation energy Delta H-f. The formation energy of V-Cu is very similar in both types of alloy compounds, while the formation energy of V-In in CuIn(S1-xSex)(2) is roughly the average value of the formation energies of V-Zn and V-Sn in Cu2ZnSn(S1-xSex)(4). Moreover, we find that the vacancy formation energies are larger in the S-rich compounds compared with the corresponding vacancies in the Se-rich compounds. The results suggest that the concentration of especially V-Cu can, to some extent, be controlled by anion alloying. (C) 2012 Elsevier B.V. All rights reserved.