Comparative study of structural and electronic properties of Cu-based multinary semiconductors

We present a systematic and comparative study of the structural and electronic properties of Cu-based ternary and quaternary semiconductors using first-principles electronic structure approaches. The important role that Cu d electrons play in determining their properties is illustrated by comparing results calculated with different exchange--correlation energy functionals. We show that systematic improvement of the calculated anion displacement can be achieved by using the Heyd-Scuseria-Ernzerhof (HSE06) functional compared with the Perdew-Burke-Ernzerhof (PBE) functional. Quasiparticle band structures are then calculated within the G⁰{W}⁰$ approximation using the crystal structures optimized within the HSE06 functional and starting from the PBE+$U$ mean-field solution. Both the calculated quasiparticle band gaps and their systematic variation with chemical constituents agree well with experiments. We also predict that the quasiparticle band gap of the prototypical semiconductor Cu₂ZnSnS₄ in the kesterite phase is 1.65 eV and that the gap of the stannite phase is 1.40 eV. These results are consistent with available experimental values, which vary from 1.45 to 1.6 eV.