Role of self-trapping in luminescence and $p$-type conductivity of wide-band-gap oxides*

Using hybrid functional calculations, we investigate the behavior of holes in the valence band of a range of wide-band-gap oxides including ZnO, MgO, In$_2$O$_3$, Ga$_2$O$_3$, Al$_2$O$_3$, SnO$_2$, SiO$_2$, and TiO$_2$. We find that, due to the orbital composition of the valence band, holes tend to form localized small polarons with characteristic lattice distortions, even in the absence of defects or impurities. These self-trapped holes (STHs) are energetically more favorable than delocalized, free holes in the valence band in all materials but ZnO and SiO$_2$. Based on calculated optical absorption and emission energies we show that STHs provide an explanation for the luminescence peaks that have been observed in many of these oxides. Additionally, we demonstrate that polaron formation prohibits $p$-type conductivity in this class of materials.