Phonons and lattice dielectric properties of zirconia

We have performed a first-principles study of the structural and vibrational properties of the three low-pressure (cubic, tetragonal, and especially monoclinic) phases of ${\mathrm{ZrO}}_2,$ with special attention to the computation of the zone-center phonon modes and related dielectric properties. The calculations have been carried out within the local-density approximation using ultrasoft pseudopotentials and a plane-wave basis. The fully relaxed structural parameters are found to be in excellent agreement with experimental data and with previous theoretical work. The total-energy calculations correctly reproduce the energetics of the ${\mathrm{ZrO}}_2$ phases, and the calculated zone-center phonon frequencies yield good agreement with the infrared and Raman experimental frequencies in the monoclinic phase. The Born effective charge tensors are computed and, together with the mode eigenvectors, used to decompose the lattice dielectric susceptibility tensor into contributions arising from individual infrared-active phonon modes. This work has been partially motivated by the potential for ${\mathrm{ZrO}}_2$ to replace ${\mathrm{SiO}}_2$ as the gate-dielectric material in modern integrated-circuit technology.