Formation energies of sodium-related point defects and dumbbell in CIS as a function of Fermi energy. At the Cu-rich limit, the corresponding chemical potentials for In and Se are and . At the Cu-poor limit, the chemical potentials are , , and . The chemical potential for sodium is that of metallic bcc sodium. The dotted lines give error estimates for the formation energies at each Fermi level position. The dashed line marks the band gap obtained with HSE06.
Kohn-Sham band structures for bulk CIS, , , and . The occupied levels are drawn in dark blue and the unoccupied levels in light blue. The dashed lines illustrate the defect-induced levels compared to the bulk band structure for and .
Diffusion paths of Na-related defects in CIS. The red stars and open circles represent values calculated with HSE06 and PBE-GGA, respectively. Thedotted lines are guides to the eye.
Binding energies (Eb ) of Na-related defect complexes. The charge states of the isolated defects are 1– for , 0 for , and 1+ for Na i .
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