Thermodynamics and kinetics of the copper vacancy in CuInSe2, CuGaSe2, CuInS2, and CuGaS2 from screened-exchange hybrid density functional theory

Abstract

Formation enthalpies and migration barriers of the copper vacancy in CuInSe2, CuGaSe22, CuInS2, and CuGaS2 are calculated by means of density functional theory with a screened-exchange hybrid functional of the Heyd–Scuseria–Ernzerhof type. The band gaps of all chalcopyrite phases are very well described by the hybrid functional using a single value for the Hartree–Fock screening parameter. The defect formation enthalpies of the copper vacancy in CuInS2 and CuGaS2 are around 0.8 eV higher than in CuInSe2 and CuGaSe2. This results in the absence of Fermi-level pinning for CuInS2 and explains a reduced tendency of CuInS2 and CuGaS2 to form ordered defect compounds. The calculated migration barrier of the copper vacancy in CuInSe2 is 1.26 eV and of comparable magnitude for CuGaSe2, CuInS2, and CuGaS2. From this data we estimate a diffusion coefficient for CuInSe2 and show that it is in agreement with measurements of diffusion in stoichiometric single crystalline samples when direct experimental methods are used.