Direct View at Excess Electrons in ${\mathrm{TiO}}_2$ Rutile and Anatase

A combination of scanning tunneling microscopy and spectroscopy and density functional theory is used to characterize excess electrons in ${\mathrm{TiO}}_2$ rutile and anatase, two prototypical materials with identical chemical composition but different crystal lattices. In rutile, excess electrons can localize at any lattice Ti atom, forming a small polaron, which can easily hop to neighboring sites. In contrast, electrons in anatase prefer a free-carrier state, and can only be trapped near oxygen vacancies or form shallow donor states bound to Nb dopants. The present study conclusively explains the differences between the two polymorphs and indicates that even small structural variations in the crystal lattice can lead to a very different behavior.

Figure 1

Calculated polaronic stability for bulk ${\mathrm{TiO}}_2$ rutile and anatase. (a) Configuration coordinate diagram showing the polaronic ($E_{\text{POL}}$), lattice ($E_{\text{ST}}$), and electronic ($E_{\text{EL}}$) energies as a function of lattice distortion for the polaronic and delocalized solution. (b) $E_{\text{POL}}$ as a function of Hubbard $U$ in bulk rutile (orange) and anatase (blue). The vertical line indicates the ab initio $U^{\text{cRPA}}$. Orbitally decomposed density of states (DOS) in rutile (c) and anatase (d), aligned with respect to the Ti core levels.

Figure 2

Local electronic structure of rutile (110) (left) and anatase (101) (right) surfaces doped by surface oxygen vacancies. Constant-height scanning tunneling microscopy images of (a),(b) empty states and (c),(d) filled states of the same areas. $V_{\mathrm{O}}$ marks surface oxygen vacancies; they are also marked with circles in (c). (e),(f) Line profiles along the lines in (a) and (b), respectively. STS measured above $V_{\mathrm{O}}$ and above regular fivefold coordinated ${\mathrm{Ti}}_{5c}$ surface atoms of (g) rutile and (h) anatase. Photoemission spectra ($h\nu =120\mathrm{eV}$, dashed lines) are included for comparison. Rutile at $T=78\mathrm{K}$, anatase at $T=6\mathrm{K}$.

Figure 3

Surface calculations of excess electrons in rutile (110) and anatase (101) donated by a surface $V_{\mathrm{O}}$. In rutile, small polarons can assume many energetically almost equivalent positions. (a) Configurations with two subsurface polarons $P_{\mathrm{sub}}$ (top) and one $P_{\mathrm{sub}}$ plus one surface polaron $P_{\text{surf}}$ (bottom). (b) The only stable configuration at the anatase surface, with both excess electrons bound to the surface $V_{\mathrm{O}}$. (c) Polaron dynamics in rutile (orange) and anatase (blue) and corresponding statistical analysis for rutile. The small polarons stay mostly in the subsurface ($S-1$) below the vacancy and at surface ($S$) ${\mathrm{Ti}}_{5c}$ sites. (d)–(g) Calculated STM images for empty (d),(e) and filled (f),(g) states in rutile (left, the three most frequent polaronic configurations according to the MD analysis) and anatase (right, the electron is always trapped at the surface $V_{\mathrm{O}}$).

Figure 4

Shallow donor state at Nb-doped anatase (101). (a) Empty and (b) filled states STM images taken at $T=6\mathrm{K}$ (constant height). The bright areas are in the vicinity to subsurface dopants. The inset “DFT” in (b) shows a calculated STM image of the shallow donor state. The electron wave function is more extended along the [010] (12–25 Å), then along the [101] (4–8 Å) direction. (c) Spatially resolved plot of $(dI/dV)/(I/V)$ along the blue dashed line. (Note the different energy scale as compared to Fig. 2.) (d) Model of the shallow donor state.