Correlation of intrinsic point defects and the Raman modes of cuprous oxide

The Raman spectrum of crystalline $\mathrm{Cu}{}_{2}\mathrm{O}$ taken off resonance is reproducible and independent of the growth method and conditions employed. But, in contrast to most other crystalline materials, the Raman spectrum of $\mathrm{Cu}{}_{2}\mathrm{O}$ is dominated by infrared active and silent lattice modes rather than by the only Raman allowed phonon mode. We show that this unusual behavior is most likely caused by the presence of copper vacancies in the so-called split configuration, a point defect particular to $\mathrm{Cu}{}_{2}\mathrm{O}$. The reduction of symmetry due to the presence of point defects may lift the Raman selection rules and may introduce Raman activity for phonon modes that are Raman forbidden in the case of perfect crystal symmetry. Based on this group theoretical consideration, we predict the angle dependence of the Raman intensities of all $\mathrm{Cu}{}_{2}\mathrm{O}$ one-phonon modes at $k=0$ for rotation about the (100) direction caused by the presence of various intrinsic point defects. Of all intrinsic defects in question, only the presence of the copper vacancy in the split configuration introduces Raman activity for all $\mathrm{Cu}{}_{2}\mathrm{O}$ extended phonon modes observed in experiment and is consistent with the angle-dependent measurements. Our study underlines the special role of the split vacancy in $\mathrm{Cu}{}_{2}\mathrm{O}$.