(Sub)Surface Mobility of Oxygen Vacancies at the ${\mathrm{TiO}}_2$ Anatase (101) Surface

Anatase is a metastable polymorph of ${\mathrm{TiO}}_2$. In contrast to the more widely studied ${\mathrm{TiO}}_2$ rutile, O vacancies ($V_{\mathrm{O}}$’s) are not stable at the anatase (101) surface. Low-temperature STM shows that surface $V_{\mathrm{O}}$’s, created by electron bombardment at 105 K, start migrating to subsurface sites at temperatures $\ge 200\mathrm{K}$. After an initial decrease of the $V_{\mathrm{O}}$ density, a temperature-dependent dynamic equilibrium is established where $V_{\mathrm{O}}$’s move to subsurface sites and back again, as seen in time-lapse STM images. We estimate that activation energies for subsurface migration lie between 0.6 and 1.2 eV; in comparison, density functional theory calculations predict a barrier of ca. 0.75 eV. The wide scatter of the experimental values might be attributed to inhomogeneously distributed subsurface defects in the reduced sample.

Figure 1

STM images ($T_{\mathrm{sample}}=78\mathrm{K}$) of ${\mathrm{TiO}}_2$ anatase (101). (a) Freshly prepared surface. (b) After irradiation with 500 eV electrons, which creates surface O vacancies ($V_{\mathrm{O}}$’s). The insets (b1) and (b2) show a magnified experimental and calculated STM image of a $V_{\mathrm{O}}$, respectively. Images obtained after annealing the sample for 10 min to (c) 326 K and (d) 450 K.

Figure 2

Stability of surface $V_{\mathrm{O}}$’s created by electron beam bombardment. The plot shows the density of $V_{\mathrm{O}}$’s after heating the sample to various temperatures for 10 min, normalized to the initial value after electron irradiation at 105 K. The dashed line shows the expected behavior assuming one $E_{\mathrm{act}}$ of 0.75 eV. The solid line assumes the trapezoidal distribution of $E_{\mathrm{act}}$’s from 0.6 to 1.2 eV displayed in the inset.

Figure 3

(Color online) Results from time-lapse STM images of surface $V_{\mathrm{O}}$’s on anatase (101). (a) Series of images ($4\times 4{\mathrm{nm}}^2$; $+1.6\mathrm{V}/0.2\mathrm{nA}$) recorded at $T=259\mathrm{K}$; the time between images was 3.2 min. The arrows mark a $V_{\mathrm{O}}$ that disappears and reappears at the same position. (b) Total defect density in time-lapse images; each trace corresponds to a separate experimental run at the sample temperature indicated. (c) Defect mobility, represented by the number of hopping events per defect and frame for different temperatures.