Optical properties of TixSi1−xO2 solid solutions

Abstract

In this work, we use density functional theory to predict the optical properties of ${\mathrm{Ti}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ solid solutions. The special quasirandom structure method and the simulated annealing procedure were applied to produce models of crystalline and amorphous ${\mathrm{Ti}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$. These were fully structurally optimized by using the vasp package, while their electronic structure and optical properties were subsequently calculated by using the wien2k package employing the TB-mBJ potential. The calculated band gaps for a-${\mathrm{Ti}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ evaluated by using the Tauc-like fitting approach are 8.53 eV for ${\mathrm{SiO}}_{2}$, quickly decreasing to 4.0 eV at $x=0.19$, 3.52 eV at $x=0.34$, and 3.24 eV for ${\mathrm{TiO}}_{2}$. Experimental samples were prepared by means of plasma-enhanced chemical vapor deposition to support the calculations. Ellipsometry and spectrophotometry yield a compositional trend for the experimental optical band gap comparable with our predictions: a quick decrease from 7.94 eV for pure ${\mathrm{SiO}}_{2}$ to 3.91 eV at $x=0.15$, followed by a much slower decrease over the rest of the composition range ending at 3.26 eV for pure ${\mathrm{TiO}}_{2}$. A detailed analysis of anatase and rutile-based solid solutions reveals the introduction of silicon-induced oxygen states into the band gap in the ${\mathrm{TiO}}_{2}$-rich composition region, which results in the predicted reduction of the band gap. However, we show that the optical absorption of those states is negligible. We have obtained good agreement between the calculated and measured imaginary part of the dielectric function ${\ensuremath{\varepsilon}}_{i}$, especially for the ${\mathrm{TiO}}_{2}$-rich compositions. Finally, we predict an almost-linear refractive index change at 632.8 nm between a-${\mathrm{SiO}}_{2}$ (1.36) and a-${\mathrm{TiO}}_{2}$ (2.34), which was experimentally confirmed.