Figure 3. Calculated formation enthalpies of H_O⁺ (blue lines) and H-DX⁻ (red lines) in ZnO as a function of Fermi level, assuming H-rich and O-poor condition.

We also show those of the separated H_i⁺ and V_O defects (H_O⁺ → H_i⁺+V_O⁰ and H_O⁺ → H_i⁺ + V_O⁰ + 2e by (gray)-dashed lines). The vertical solid lines indicate the VBM and the CBM, and the vertical (green) solid-line indicates the pinning position of Fermi-level (ε_pin). The calculational details are written in supplementary information.