We report on experimental results on band gap and lattice distortion in CuInSe${}_2$ for various degrees of Cu deficiency. The band gap is measured by optical methods, and the Cu vacancy density and anion displacement parameter are determined by neutron scattering. Our data show that the band gap decreases for Cu-poor compositions, and the anion displacement is weakly dependent on the concentration of Cu vacancies. This is in apparent contradiction with ab initio calculations that always predict a larger band gap in presence of Cu vacancies. To shed light on this issue, we studied the overall dependence of the band gap on the anion displacement and on the concentration of Cu vacancies using a self-consistent $GW$ approach and hybrid functionals, including a feedback mechanism that was recently proposed. Our calculations illustrate consistently the remarkable stability of the band gap of chalcopyrite semiconductors and explain the experimental observations by a coupled effect of Cu vacancies and lattice distortions within the feedback model.

• Received 23 September 2011

DOI:https://doi.org/10.1103/PhysRevB.86.045216