Band structure and phase stability of the copper oxides Cu 2 O, CuO, and Cu 4 O 3

The $p$-type semiconductor copper oxide has three distinct phases Cu${}_{2}$O, CuO, and Cu${}_{4}$O${}_{3}$ with different morphologies and oxidation states of the copper ions. We investigate the structural stability and electronic band structure of all three copper oxide compounds using ab initio methods within the framework of density functional theory and consider different exchange correlation functionals. While the local density approximation (LDA) fails to describe the semiconducting states of CuO and Cu${}_{4}$O${}_{3}$, the $\mathrm{LDA}+U$ and HSE06 hybrid functional describe both compounds as indirect semiconductors. Using the HSE06 hybrid functional we calculate the electronic band structure in the full Brillouin zone for all three copper oxide compounds.