Indium oxide is widely used as a transparent conducting oxide. Interstitial hydrogen $\left({\mathrm{H}}_i\right)$ acts as a shallow donor, but is expected to be quite mobile, thus enabling potential applications in electrochemical synapses or electrochemical random-access memory. Understanding the diffusion of interstitial hydrogen is essential for controlling its incorporation and stability. Using first-principles calculations based on hybrid density functional theory we find that the proton is the most stable charge state for Fermi levels up to 0.77 eV above the conduction-band minimum. Based on the nudged elastic band method we find that local hopping of the H atom, corresponding to a realignment of the O-H bond, can occur with an activation energy of 0.24 eV; this process can thus occur at low temperatures but does not lead to long-range diffusion. The long-range migration path of ${\mathrm{H}}_i^{+}$ can be decomposed into rotations of the hydrogen atom around oxygen atoms and jumps between two oxygen atoms, with an overall activation energy of 0.94 eV. We compare our results with recent experiments, finding excellent agreement in both the low-temperature and high-temperature regimes, but leading to a re-evaluation of the measured activation energy. Our results provide insight into the different physical mechanisms that govern hydrogen motion in the different temperature regimes, and highlight the necessity of including the quantum-mechanical behavior of protons at low temperature.

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• Defects
• Ionic transport
• Transparent conducting oxides
• Density functional calculations