Realistic computer models of amorphous ZrO2 : Ta2O5 : Structural, optical, and vibrational properties

Amorphous zirconia-alloyed-tantala (${\mathrm{ZrO}}_{2}$:${\mathrm{Ta}}_{2}{\mathrm{O}}_{5}$) is of interest as a prospective coating material to make the highly reflective mirrors used in gravitational wave detectors. We study the atomic structure of thin films of ${\mathrm{ZrO}}_{2}$:${\mathrm{Ta}}_{2}{\mathrm{O}}_{5}$ by making realistic computer models using force enhanced atomic refinement. The models are, by construction, in agreement with measured x-ray scattering functions. The models made with x-ray scattering data on as-deposited and 800 \ifmmode^\circ\else\textdegree\fi{}C-annealed samples showed clear structural differences, particularly in their metal-metal correlation. The ratio of corner-shared to edge-shared polyhedra increased as a result of annealing. The electronic band gap and the density of states of ${\mathrm{ZrO}}_{2}$:${\mathrm{Ta}}_{2}{\mathrm{O}}_{5}$ are found to be similar to that of pure ${\mathrm{Ta}}_{2}{\mathrm{O}}_{5}$ and remained unchanged upon annealing. We used the Hyed-Scuseria-Ernzerhof hybrid functional to estimate the band gap of ${\mathrm{ZrO}}_{2}$:${\mathrm{Ta}}_{2}{\mathrm{O}}_{5}$ to be $\ensuremath{\approx}$ 4 eV, which is close to the experimental band gap of pure ${\mathrm{Ta}}_{2}{\mathrm{O}}_{5}$. The refractive indexes calculated from the models were in reasonable agreement with the experiment. Vibrational modes at high frequencies involve highly localized bond stretch modes associated with a corner-shared O atom connecting two metal-oxygen polyhedra.