Band-gap engineering in TiO${}_2$-based ternary oxides

The electronic structure of several ternary oxides (Sn${}_2$TiO${}_4$, PbTiO${}_3$, Bi${}_2$Ti${}_4$O${}_{11}$, and Bi${}_4$Ti${}_3$O${}_{12}$) based on binary lone-pair oxides (SnO, PbO, and Bi${}_2$O${}_3$) and a $d$${}^0$ oxide (TiO${}_2$) is investigated using soft x-ray spectroscopy and electronic-structure calculations. We find that the valence band of these ternary oxides is bounded by bonding (at the bottom of the valence band) and antibonding (at the top of the valence band) O 2p lone-pair $ns$ (Sn $5s$, Pb $6s$, Bi $6s$) hybridized states, while the conduction band is dominated by unoccupied Ti $3d$ states. The existence of these two features is found to be independent of crystal structure or stoichiometry. The calculated hybridization in the bonding O $2p$ lone-pair $ns$ states is in reasonable agreement with the relative intensity of this feature in the measured x-ray emission spectra. The dominant influence on the conduction and the valence bands in the ternary oxides is due to different aspects of the electronic structure in the parent binary oxides, and we consequently find that the band gap of the ternary oxide is found to be a stoichiometric-weighed addition of the band gaps of the parent oxides.

Figure 1

Crystal structures of the oxides studied herein. (a) PbTiO${}_3$, (b) Bi${}_4$Ti${}_3$O${}_{12}$, (c) SnO or PbO, (d) TiO${}_2$, (e) Bi${}_2$O${}_3$, (f) Sn${}_2$TiO${}_4$, (g) Bi${}_2$Ti${}_4$O${}_{11}$. In the case of Bi${}_4$Ti${}_3$O${}_{12}$, only half of the unit cell is shown; the full unit cell is formed by mirroring the shown atoms upward in the plane of the page. In the other cases, slightly more than a single unit cell is shown to emphasize the site symmetry of the cations. These crystal structure diagrams were produced using vesta 2.1.0 (Ref. 36).

Figure 2

Calculated DOS of the materials studied herein. The top of the valence band is at 0 eV. (For brevity, we will call the top of the valence band the “Fermi level,” even though technically the Fermi level is undefined for band-gap materials.) The calculations predict that all materials have a band gap, although the gap for SnO is quite small. The conduction-band Ti $3d$ states have been reduced in amplitude by a factor of 3. Note how the lone-pair cation states (Sn $5s$, Pb, and Bi $6s$) are split into bonding and antibonding states at the bottom and top of the valence band, respectively.

Figure 3

Measured and calculated O $k$ XES and $1s$ XAS spectra of the materials studied herein. The calculated spectra were shifted so the main O $K$ XES peak was aligned with the experimental peak. The key spectral features (labeled $S$${}_1$, $A$, $B$, $S$${}_2$, $C$, and $D$) are denoted by small black lines on each spectrum. Note TiO${}_2$ lacks the $S$${}_{1,2}$ XES features, while SnO, PbO, and Bi${}_2$O${}_3$ lack the $C$, $D$ XAS features.

Figure 4

(a) $f_{\text{O}2p}$ derived from the XES compare to the calculated DOS hybridization [O $2p/(\mathrm{O}2p+\mathrm{cation}ns$) using the calculated DOS]. The error bars denote the approximate spread of $f_{\text{O}2p}$ if the estimated end of region $S_1$ is shifted by $\pm$0.2 eV, the straight line indicates perfect agreement between $f_{\text{O}2p}$ and the DOS hybridization. (b) The calculated band gaps (G${}_{\mathrm{mBJ}}$, top) and estimated spectral gaps (${\Delta }_{\exp }$, bottom) for these materials, expressed as a fraction of the TiO${}_2$ content. The lines indicate a linear change in gap with TiO${}_2$ content. (c) The energy of the measured XES spectral features as a function of TiO${}_2$ content the lines of the Fermi level and the bottom of the conduction band estimated using the second derivative maxima.