Calculations of strain-modified anatase ${\text{TiO}}_2$ band structures

In order to theoretically quantify a strain-inducing method that we use to engineer the material properties of anatase titania, we studied its electronic band structure over a range of biaxial strain by utilizing both the density functional theory within the generalized gradient approximation (GGA) and quasiparticle theory calculations within the GW approximation. This strain-modified material is suitable for use as a high efficiency photoanode in a photoelectrochemical cell. We track the changes to the band gap and the charge carrier effective masses versus the total pressure associated with the strained lattice. Both the GGA and the GW approximation predict a linear relationship between the change in band gap and the total pressure. However, the GGA underestimates the slope by more than 57% with respect to the GW approximation result of 0.0685 eV/GPa. We also compare our predicted band gap shift to a reported experimental result.

Figure 1

Plot of the two bands containing the CBM and VBM along $\Delta$. The effective mass calculations are based on the dashed curves. The minimum band gap is indirect with the CBM at $\Gamma$ and the VBM at $0.86\Delta$. The solid points are indicators of where GW correction data are available.

Figure 2

Band structure plot for the equilibrium anatase ${\text{TiO}}_2$ lattice.

Figure 3

Derivative of the band gap with respect to the total pressure. GGA and GW approximation results of the indirect gap between $\Gamma$ and $2/3\Delta$.

Figure 4

Effective mass of the charge carriers vs the total pressure.

Figure 5

Maximum achievable solar-to-hydrogen conversion efficiency vs total pressure.