Importance of surface oxygen vacancies for ultrafast hot carrier relaxation and transport in Cu$_2$O

Cu$_2$O has appealing properties as an electrode for photo-electrochemical water splitting, yet its practical performance is severely limited by inefficient charge extraction at the interface. Using hybrid DFT calculations, we investigate carrier capture processes by oxygen vacancies (V$_\mathrm{O}$) in the experimentally observed ($\sqrt{3} \times \sqrt{3}$)R30$^{\circ}$ reconstruction of the dominant (111) surface. Our results show that these V$_\mathrm{O}$ are doubly ionized and that associated defects states strongly suppress electron transport. In particular, the excited electronic state of a singly charged V$_\mathrm{O}$ plays a crucial role in the non-radiative electron capture process with a capture coefficient of about 10$^{-9}$~cm$^3$/s and a lifetime of 0.04~ps, explaining the experimentally observed ultrafast carrier relaxation. These results highlight that engineering the surface V$_\mathrm{O}$ chemistry will be a crucial step in optimizing Cu$_2$O for photoelectrode applications.