Hydrogen centers and the conductivity of $\mathrm{I}{\mathrm{n}}_2{\mathrm{O}}_3$ single crystals

A series of infrared absorption experiments and complementary theory have been performed to determine the properties of OH and OD centers in $\mathrm{I}{\mathrm{n}}_2{\mathrm{O}}_3$ single crystals. Annealing $\mathrm{I}{\mathrm{n}}_2{\mathrm{O}}_3$ samples in ${\mathrm{H}}_2$ or ${\mathrm{D}}_2$ at temperatures near 450 °C produces an $n-\text{type}$ layer $\approx 0.06\mathrm{mm}$ thick with an $n-\text{type}$ doping of $1.6\times {10}^{19}\mathrm{c}{\mathrm{m}}^{-3}$. The resulting free-carrier absorption is correlated with an OH center with a vibrational frequency of $3306\mathrm{c}{\mathrm{m}}^{-1}$ that we associate with interstitial ${\mathrm{H}}^{+}$. Additional O-H (O-D) vibrational lines are assigned to metastable configurations of the interstitial ${\mathrm{H}}^{+}\left({\mathrm{D}}^{+}\right)$ center and complexes of H (D) with In vacancies. Unlike other oxides studied recently where H trapped at an oxygen vacancy is the dominant shallow donor (ZnO and $\mathrm{Sn}{\mathrm{O}}_2$, for example), interstitial ${\mathrm{H}}^{+}$ is found to be the dominant H-related shallow donor in $\mathrm{I}{\mathrm{n}}_2{\mathrm{O}}_3$.

Figure 1

A selection of IR absorption spectra ($T=4.2\mathrm{K}$, resolution = $1\mathrm{c}{\mathrm{m}}^{-1}$) for an $\mathrm{I}{\mathrm{n}}_2{\mathrm{O}}_3$ sample that initially had been hydrogenated by an anneal (30 min) in an ${\mathrm{H}}_2$ ambient at 500 °C. The sample was then annealed sequentially in flowing He at the temperatures shown in degrees Celsius. (a) Absorption due to free carriers. (b) IR absorption lines in the O-H stretching region. These spectra were baseline corrected to remove the contribution from free carriers.

Figure 2

IR absorption spectra (4.2 K, resolution = $1\mathrm{c}{\mathrm{m}}^{-1}$) for $\mathrm{I}{\mathrm{n}}_2{\mathrm{O}}_3$ samples containing D and H. Spectra were baseline corrected to remove the contribution from free carriers. The sample for the upper spectrum in (a) had been deuterated by annealing in a ${\mathrm{D}}_2$ ambient (60 min) at 500 °C. It was then annealed in flowing He at 550 °C to increase its transparency and to produce the O-D lines that are shown. The sample for the upper spectrum in (b) had been hydrogenated by annealing (30 min) in an ${\mathrm{H}}_2$ ambient at 500 °C and subsequently annealed (30 min) at 550 °C. [The lower spectrum in (a) shows the D-stretching region for a hydrogenated sample, and the lower spectrum in (b) shows the H-stretching region for a deuterated sample.]

Figure 3

A selection of IR absorption spectra ($T=77\mathrm{K}$, resolution = $1\mathrm{c}{\mathrm{m}}^{-1}$) for an $\mathrm{I}{\mathrm{n}}_2{\mathrm{O}}_3$ sample that initially had been annealed (60 min) in flowing He at 850 °C to remove any hydrogen that might have been present and was subsequently deuterated by an anneal (30 min) in an ${\mathrm{D}}_2$ ambient at 500 °C. The sample was then annealed sequentially in flowing He at the temperatures shown in °C. (a) Absorption due to free carriers. (Free-carrier absorption spectra measured following anneals from 50 to 250 °C are indistinguishable from the results shown for the D-treated sample and also following the anneal at 200 °C.) (b) IR absorption lines in the O-D stretching region. These spectra were baseline corrected to remove the contribution from free carriers.

Figure 4

A selection of IR absorption spectra ($T=77\mathrm{K}$, resolution = $1\mathrm{c}{\mathrm{m}}^{-1}$) for an $\mathrm{I}{\mathrm{n}}_2{\mathrm{O}}_3$ sample that initially had been annealed (30 min) in flowing He at 1000 °C to remove any hydrogen that might have been present and was subsequently hydrogenated by an anneal (30 min) in an ${\mathrm{H}}_2$ ambient at 450 °C. The sample was then sequentially thinned by lapping and polishing the front and back surfaces. The thickness removed following each thinning step (both sides) is shown in mm. (a) Free-carrier absorption spectra for the H-treated sample and for the sample following thinning. (b) Baseline-corrected IR spectra of the O-H absorption lines.

Figure 5

Strength of free-carrier absorption and O-H vibrational absorption for the $\mathrm{I}{\mathrm{n}}_2{\mathrm{O}}_3$ sample whose IR data are shown in Fig. 4 as a function of thickness removed from the sample. The left scale (filled circles) shows the difference in the free-carrier absorption at 2500 and $4000\mathrm{c}{\mathrm{m}}^{-1}$ for each thickness removed. The right scale (open circles) shows the integrated absorbance for the $3306\mathrm{c}{\mathrm{m}}^{-1}$ O-H stretching line assigned to the interstitial ${\mathrm{H}}^{+}$ shallow donor for each thickness removed.

Figure 6

IR absorption spectrum ($T=4.2\mathrm{K}$, resolution = $1\mathrm{c}{\mathrm{m}}^{-1}$) for an $\mathrm{I}{\mathrm{n}}_2{\mathrm{O}}_3$ sample deuterated by an anneal (60 min) in a ${\mathrm{D}}_2$ ambient at 500 °C.

Figure 7

Selection of IR absorption spectra ($T=77\mathrm{K}$, resolution = $1\mathrm{c}{\mathrm{m}}^{-1}$) for an as-grown $\mathrm{I}{\mathrm{n}}_2{\mathrm{O}}_3$ sample that was gray in color. The sample was annealed sequentially in flowing He at the temperatures shown in °C. (a) Absorption due to free carriers. (b) IR absorption lines in the O-H stretching region. These spectra were baseline corrected to remove the contribution from free carriers.

Figure 8

Defect models. (a) Lowest energy AB configuration $\left(\mathrm{A}{\mathrm{B}}_{01}\right)$ for ${\mathrm{H}}_{\mathrm{i}}^{+}$. (b) Metastable ${\mathrm{H}}_{\mathrm{i}}^{+}$ AB configurations ($\mathrm{A}{\mathrm{B}}_{02}$ to $\mathrm{A}{\mathrm{B}}_{04}$). Defect labeling follows Ref. [12]. (c) Lowest energy configuration for ${[V_{\mathrm{In}}\left(24d\right)-\mathrm{H}]}^{2-}$. Larger (blue) atoms represent O, smaller (black) atoms represent In, and the smallest (red) atom is H. This was constructed by MOLDRAW (P. Ugliengo, Torino 2006, available at http://www.moldraw.unito.it) and POV-Ray (http://povray.org).