Formation enthalpies and migration barriers of the copper vacancy in CuInSe2, CuGaSe22, CuInS2, and CuGaS2 were 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 were 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 were around 0.8eV higher than in CuInSe2 and CuGaSe2. This results in the absence of Fermi-level pinning for CuInS2 and explained a reduced tendency of CuInS2 and CuGaS2 to form ordered defect compounds. The calculated migration barrier of the copper vacancy in CuInSe2 was 1.26eV and of comparable magnitude for CuGaSe2, CuInS2, and CuGaS2. From these data, a diffusion coefficient for CuInSe2 was estimated and it was shown that it was in agreement with measurements of diffusion in stoichiometric single crystalline samples when direct experimental methods were used.

Thermodynamics and Kinetics of the Copper Vacancy in CuInSe2, CuGaSe2, CuInS2, and CuGaS2 from Screened-Exchange Hybrid Density Functional Theory. J.Pohl, K.Albe: Journal of Applied Physics, 2010, 108[2], 023509