Thermodynamics and kinetics of the copper vacancy in CulnSe_2, CuGaSe_2, CulnS_2, and CuGaS_2 from screened-exchange hybrid density functional theory

摘要

Formation enthalpies and migration barriers of the copper vacancy in CuInSe_2, CuGaSe2_2, CuInS_2, and CuGaS_2 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 CuInS_2 and CuGaS_2 are around 0.8 eV higher than in CuInSe_2 and CuGaSe_2. This results in the absence of Fermi-level pinning for CuInS_2 and explains a reduced tendency of CuInS_2 and CuGaS_2 to form ordered defect compounds. The calculated migration barrier of the copper vacancy in CuInSe2 is 1.26 eV and of comparable magnitude for CuGaSe_2, CuInS_2, and CuGaS_2- From this data we estimate a diffusion coefficient for CuInSe_2 and show that it is in agreement with measurements of diffusion in stoichiometric single crystalline samples when direct experimental methods are used.