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

${\mathrm{Cu}}_2\mathrm{O}$ has appealing properties as an electrode for photoelectrochemical 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 ($\sqrt{3}\times \sqrt{3})R{30}^{\circ }$ 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 nonradiative electron capture process with a capture coefficient of about ${10}^{-9}{\mathrm{cm}}^3$/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 ${\mathrm{Cu}}_2\mathrm{O}$ for photoelectrode applications.

Figure 1

(a) Lateral and (b) top view of the stoichiometric, unreconstructed ($1\times 1$)-(111) ${\mathrm{Cu}}_2\mathrm{O}$ slab model within the ($\sqrt{3}\times \sqrt{3})R{30}^{\circ }$ supercell. ${\mathrm{O}}_{\mathrm{CUS}}$ and ${\mathrm{Cu}}_{\mathrm{CUS}}$ are the coordinatively unsaturated O and Cu surface sites, respectively, while ${\mathrm{O}}_{\mathrm{CSA}}$ and ${\mathrm{O}}_{\mathrm{CSA}}$ indicate the coordinatively saturated O and Cu atoms. (c) Top view of the reconstructed ($\sqrt{3}\times \sqrt{3})R{30}^{\circ }$-(111) ${\mathrm{Cu}}_2\mathrm{O}$ slab model with one oxygen vacancy ($V_{\mathrm{O}}$). ${\mathrm{Cu}}_{\mathrm{NN}}$ are Cu sites adjacent to $V_{\mathrm{O}}$.

Figure 2

Density of states for the ($\sqrt{3}\times \sqrt{3})R{30}^{\circ }$ supercell (a) in the stoichiometric case and with one (b) $V_{\mathrm{O}}^{••}$, (c) $V_{\mathrm{O}}^{•}$, and (d) $V_{\mathrm{O}}^{\mathrm{X}}$. The zero of the energy scale was set at the Fermi energy. For the spin-polarized $V_{\mathrm{O}}^{•}$ calculation, the DOS for the spin-up and spin-down channels are reported with positive and negative values respectively on the $y$ axis. The isosurfaces (2$\times {10}^{-2} e/{\AA }^3$) in (e)–(h) correspond to the charge density associated with the defect states (DS) or surface states (SS) highlighted with the corresponding color in plots (a)–(d). (i) Oxygen vacancy formation energy $[E_f\left(V_{\text{O}}\right)$] under O-poor conditions in different charge states as a function of the Fermi energy ranging from the valence band maximum ($E_F=0$) up to the experimental band gap for the ${\mathrm{Cu}}_2\mathrm{O}$-(111) surface.

Figure 3

Configuration coordinate diagram for $V_{\mathrm{O}}$($+$2/$+$1) carrier capture at the reconstructed ${\mathrm{Cu}}_2\mathrm{O}$-(111) surface. The solid circles represent the relative formation energies calculated using hybrid DFT and lines are spline fits. $\mathrm{\Delta }{E}_{\mathrm{b}}$ are carrier capture barriers.

Figure 4

Schematic representation of electron capture at the reconstructed ($\sqrt{3}\times \sqrt{3})R{30}^{\circ } {\mathrm{Cu}}_2\mathrm{O}$-(111) surface. Due to surface band bending photoexcited electrons drift towards the surface, where they can either drive photocatalytic reactions (not shown) or be trapped in surface defect states (DS), if available. DS shown in the schematic result from experimentally observed surface oxygen vacancies ($V_{\mathrm{O}}$). Direct trapping into DS1 or DS2 is slow, but an electron can very rapidly be trapped into an excited state DS2*, from where it can relax into either DS1 or DS2. Blue and red spheres represents Cu and O atoms, respectively, while ${\mathrm{V}}_{\mathrm{O}}$ are shown in orange.

Figure 5

Comparison of the experimentally measured (dashed lines) and computed (solid lines) density of states for (a) the stoichiometric ($1\times 1$) and (b) the reconstructed ($\sqrt{3}\times \sqrt{3}$)-$R$30${}^{\circ }$-(111) ${\mathrm{Cu}}_2\mathrm{O}$ surface with $V_{\mathrm{O}}$. For the valence band, determined using 1PPE, we compare with the ground-state $V_{\mathrm{O}}^{\mathrm{X}}$ DOS, whereas for the empty states, determined using 2PPE, we compare with the excited-state $V_{\mathrm{O}}^{•}$ DOS. For the spin-polarized $V_{\mathrm{O}}^{•}$ DOS, the spin-up and spin-down channels have been summed. Note the missing photoelectron signals at energies higher than 2 eV in (b).