The band structures of cubic ${\mathrm{Cu}}_2$O and monoclinic CuO crystals have been calculated by means of the first-principles orthogonalized linear combination of atomic orbitals method. Using the wave functions obtained, the frequency-dependent interband optical conductivities are also evaluated. The results show ${\mathrm{Cu}}_2$O to be a direct-gap semiconductor, while CuO is semiconductorlike with an intrinsic hole population at the top of the valence band (VB). By comparing with a variety of existing data, we conclude that band theory works extremely well for ${\mathrm{Cu}}_2$O, but is less satisfactory for CuO. This could be due to strong correlation effects for states near the top of the VB in CuO. A careful reanalysis of optical data and excitonic spectra in ${\mathrm{Cu}}_2$O in conjunction with our calculations suggests a complete reinterpretation of these data. A clear distinction between the intrinsic gap and the optical gap is argued. We conclude that the intrinsic gap in ${\mathrm{Cu}}_2$O is of the order of 0.8 eV, while the optical gap is of the order 2.0–2.3 eV. The excitonic series in ${\mathrm{Cu}}_2$O is due to the Coulombic attraction of the hole at the top of the VB and the electron in the next-higher conduction band (CB), not the lowest CB, because of the forbidden symmetry associated with angular-momentum conservation. This reinterpretation of the excitonic data is also consistent with a calculated low value for the static dielectric constant ${\epsilon }_0$ of order of 4 for ${\mathrm{Cu}}_2$O.

• Received 7 March 1989

DOI:https://doi.org/10.1103/PhysRevB.40.7684