Uniaxial stress dependence of the direct-forbidden and indirect-allowed transitions of TiO2

Abstract

We have investigated the effect of uniaxial compression along the [001], [100], and [110] directions on the direct and indirect absorption edges of Ti${\mathrm{O}}_2$. Very-high-stress conditions ($X\sim 25$ kbar) have been achieved in this work, enabling us to investigate accurately all linear and nonlinear stress dependences of the corresponding band extrema. Concerning the direct-forbidden edge, we confirm our previous assignment as a ${\Gamma }_{3v}\to {\Gamma }_{1c}$ transition. We define and measure two independent deformation potentials $a_d=-2.13\mathrm{}\pm 0.02$ eV and $b_d=-3.74\mathrm{}\pm 0.04$ eV, which correspond to a hydrostatic-pressure coefficient: $\frac{d{E}_{\mathrm{gd}}}{\mathrm{dP}}=+1.17\mathrm{}\times {10}^{-6\mathrm{}}$ eV/bar. Concerning the indirect transition, we find a stress-induced splitting for [100] stress. This corresponds to a subsidiary maximum of the valence band along the $\Delta$ direction in the first Brillouin zone. The corresponding shear-deformation potential $c_v$ is deduced. We find $\left|c_v\right|=0.758\mathrm{}\pm 0.014$ eV. The two deformation potentials associated with the indirect transition are $a_i=-2.04\mathrm{}\pm 0.02$ eV and $b_i=-4.34\mathrm{}\pm 0.04$ eV, which give a pressure coefficient $\frac{d{E}_{\mathrm{gi}}}{\mathrm{dP}}=1.19\mathrm{}\times {10}^{-6\mathrm{}}$ eV/bar. Finally, we analyze the nonlinear dependence obtained for [100] stress in terms of twofold stress-induced coupling between ${\Gamma }_{3v}$ and two neighboring ${\Gamma }_1$ bands. The corresponding deformation potentials are: $\left|E_{31}\right|=7.58\mathrm{}\pm 0.14$ eV and $\left|{E^{\prime }}_{31}\right|=5.2\mathrm{}\pm 0.5$ eV.