Uncovering the Complex Behavior of Hydrogen in ${\mathrm{Cu}}_2\mathrm{O}$

The behavior of hydrogen in $p$-type ${\mathrm{Cu}}_2\mathrm{O}$ has been reported to be quite unusual. Muon experiments have been unable to ascertain the preferential hydrogen site within the ${\mathrm{Cu}}_2\mathrm{O}$ lattice, and indicate that hydrogen causes an electrically active level near the middle of the band gap, whose nature, whether accepting or donating, is not known. In this Letter, we use screened hybrid-density-functional theory to study the nature of hydrogen in ${\mathrm{Cu}}_2\mathrm{O}$, and identify for the first time the “quasiatomic” site adopted by hydrogen in ${\mathrm{Cu}}_2\mathrm{O}$. We show that hydrogen will always act as a hole killer in $p$-type ${\mathrm{Cu}}_2\mathrm{O}$, and is one likely cause of the low performance of ${\mathrm{Cu}}_2\mathrm{O}$ solar cell devices.

Figure 1

(a) Octahedral [large light gray (blue) sphere] and tetrahedral (large black sphere) interstitial positions in ${\mathrm{Cu}}_2\mathrm{O}$, (b) coordination around an O atom in ${\mathrm{Cu}}_2\mathrm{O}$, and (c) possible sites for interstitial H (${\mathrm{H}}_i^{\mathrm{BC}}$, ${\mathrm{H}}_i^{\mathrm{AB}1}$, and ${\mathrm{H}}_i^{\mathrm{AB}2}$) around the tetrahedral O in ${\mathrm{Cu}}_2\mathrm{O}$.

Figure 2

HSE ($\alpha =27.5\%$) spin density for ${\mathrm{H}}_i^{\mathrm{tet}}$ in ${\mathrm{Cu}}_2\mathrm{O}$. The small dark gray (red), large light gray (yellow), and medium-sized medium gray (green) spheres denote O, Cu, and H, respectively. The black isosurface is shown at $0.01e{\AA }^{-3}$.

Figure 3

HSE ($\alpha =27.5\%$) calculated formation energies for intrinsic $p$-type (blue), $n$-type (red), and hydrogen impurity (green) defects in ${\mathrm{Cu}}_2\mathrm{O}$ in (a) Cu-rich–O-poor conditions and (b) Cu-poor–O-rich conditions. The solid dots denote the transition levels $ϵ(q/q^{\prime })$.