Cubic ${\mathrm{TiO}}_2$ as a potential light absorber in solar-energy conversion

Materials are currently sought for use in the photo-induced decomposition of water on crystalline electrodes. Titanium dioxide is valuable in this respect. The electronic structural properties of cubic ${\mathrm{TiO}}_2$ polymorphs were investigated by means of first-principles methods. We demonstrate that both fluorite- and pyrite-type ${\mathrm{TiO}}_2$ have important optical absorptive transitions in the region of the visible light. A cubic ${\mathrm{TiO}}_2$ phase that can efficiently absorb the sunlight would be an important candidate material for the development of the solar cells. Also, we present results on the $\mathrm{Ti}$ $L$ edges for the two different titania forms. We predict that a qualitative spectroscopic discrimination of the cubic polymorphs can be achieved by following the $\mathrm{Ti}$ $2p\to 3d$ x-ray transitions.

Figure 1

(Color online) Unit cell of fluorite-structured ${\mathrm{TiO}}_2$ along the [001] plane [space group $Fm3m$ (225)]. Larger spheres represent the titanium $\left(\mathrm{Ti}\right)$ atoms, while small spheres indicate the oxygen $\left(\mathrm{O}\right)$ ions. The local-density approximation (LDA) structural parameters computed at $0\mathrm{GPa}$ are: $\mathrm{a}=4.748\mathrm{\AA }$, $\mathrm{Ti}$ (0.00,0.00,0.00), and $\mathrm{O}$ (0.25,0.25,0.25).

Figure 2

(Color online) Projection of the pyrite-type ${\mathrm{TiO}}_2$ phase along the [001] plane [space group $Pa\overline{3}$ (205)]. The computed LDA zero-pressure structural parameters are: $\mathrm{a}=4.813\mathrm{\AA }$, $\mathrm{Ti}$ (0.00,0.00,0.00), and $\mathrm{O}$ (0.34,0.34,0.34).

Figure 3

Total and partial density of states for the fluorite-structured ${\mathrm{TiO}}_2$ form given in states per eV. Insert (b) shows the crystal-field splitting of the $\mathrm{Ti}$ $3d$ electrons due to the ${\mathrm{O}}_h$ $\left(m3m\right)$ symmetry of the $\mathrm{Ti}$ site. The local coordinate system is $3\parallel \left(111\right)$, where $x,y$, and $z$ point along the original crystal axes.

Figure 4

(Color online) Density of states for the pyrite-structured ${\mathrm{TiO}}_2$ phase. Insert (b) shows the splitting of the $\mathrm{Ti}\text{−}d$ states according to the $S_6$ $\left(-3\right)$ local symmetry. The coordinate axis of titanium is $-3\parallel z$, where the $z$ axis has been moved into the (111) direction by rotating by $45°$ around both the original x and y crystal axes.

Figure 5

(Color online) Partial unoccupied $\mathrm{Ti}$ density of states for different $\mathrm{Ti}$ local symmetries. The coordinate system for rutile is $2\perp z,m\perp y$, and $2\perp x$, where both $x$ and $y$ axes have been rotated by $45°$ around the original crystal axis $z$.

Figure 6

Band structure of fluorite-structured ${\mathrm{TiO}}_2$ along high-symmetry directions of the irreducible Brillouin zone (IBZ). The valence band maximum is taken as the energy zero.

Figure 7

Band structure of pyrite-structured ${\mathrm{TiO}}_2$ along the high-symmetry directions of the cubic IBZ.

Figure 8

Calculated imaginary part of the dielectric function $\left({\epsilon }_2\right)$ for various ${\mathrm{TiO}}_2$ polymorphs. The present data were averaged over the three ($x,y$, and $z$) polarization vectors. We label the valence bands from $1\to 12\left(48\right)$ and the conduction bands from 13 (49) to upwards for fluorite (pyrite).

Figure 9

Theoretical XANES spectra at the $\mathrm{Ti}$ $L_{II,III}$ edges in various ${\mathrm{TiO}}_2$ phases. The onset energies for (b) and (c) have been adjusted with respect to rutile by accounting for the $\mathrm{Ti}$ $2p_{3∕2}^4$ core energy level shifts. All the $\mathrm{Ti}$ $L$ edges were computed by using an instrumental resolution of $0.5\mathrm{eV}$.