Determining the diffusivity of H$_{\mathrm{i}}^{\mathrm{+}}$ in In$_{\mathrm{2}}$O$_{\mathrm{3}}$ single crystals for over ten decades

Interstitial hydrogen (H$_{\mathrm{i}}^{\mathrm{+}})$ is an $n$-type dopant in In$_{\mathrm{2}}$O$_{\mathrm{3}}$ that has attracted attention for solar-cell applications [1]. An IR absorption line observed at 3306 cm$^{\mathrm{-1}}$ for In$_{\mathrm{2}}$O$_{\mathrm{3}}$ single crystals annealed in an H$_{\mathrm{2}}$ ambient has been assigned to the H$_{\mathrm{i}}^{\mathrm{+}}$ center [2]. Two types of experiments have been performed to determine the diffusivity of H$_{\mathrm{i}}^{\mathrm{+}}$ in In$_{\mathrm{2}}$O$_{\mathrm{3.}}$ At temperatures near 673 K, experiments have been performed to determine the diffusivity of H$_{\mathrm{i}}^{\mathrm{+}}$ from its indiffusion depth into In$_{\mathrm{2}}$O$_{\mathrm{3}}$. At 165 K, stress can be used to produce a preferential alignment of the H$_{\mathrm{i}}^{\mathrm{+}}$ center. With the help of theory, the kinetics with which this alignment can be produced yield the time constant for a single jump of the H$_{\mathrm{i}}^{\mathrm{+}}$ center and also the diffusivity of H$_{\mathrm{i}}^{\mathrm{+}}$ at 165 K [3]. These data determine the diffusivity for H$_{\mathrm{i}}^{\mathrm{+}}$ for over ten decades! [1] T. Koida \textit{et al.}, Jpn. J. Appl. Phys. \textbf{46}, L685 (2007). [2] W. Yin \textit{et al.}, Phys. Rev. B \textbf{91}, 075208 (2015). [3] P. Weiser \textit{et al.}, Appl. Phys. Lett., in press.