Dielectric constants of amorphous hafnium aluminates: First-principles study

Amorphous model structures of hafnium aluminate having a Hf content of 0.2 $(a\text{\ensuremath{-}}{\mathrm{Hf}}_{0.2}{\mathrm{Al}}_{0.8}{\mathrm{O}}_{1.6})$, alumina $(a\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{O}}_{3})$, and hafnia $(a\text{\ensuremath{-}}\mathrm{Hf}{\mathrm{O}}_{2})$ are theoretically generated, and dielectric responses of the amorphous model structures are studied by the first-principles method. The models have corner, edge, and face shared $\mathrm{Al}{\mathrm{O}}_{n}$ $(n=4\char21{}6)$ and $\mathrm{Hf}{\mathrm{O}}_{n}$ $(n=5\char21{}8)$ polyhedra, and the $a\text{\ensuremath{-}}{\mathrm{Hf}}_{0.2}{\mathrm{Al}}_{0.8}{\mathrm{O}}_{1.6}$ model structures are phase separated at the atomistic level, having ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ and $\mathrm{Hf}{\mathrm{O}}_{2}$ domains. Calculated dielectric constants of the models increase with increasing Hf content, and the dielectric constant increase is dominated by the lattice polarization contribution to the dielectric constant. We found that low-frequency phonon modes having a frequency less than $200\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ largely contribute to the high lattice dielectric constant and that inter-$\mathrm{Hf}{\mathrm{O}}_{2}$ domain vibrations and vibration of atoms in distorted metal-oxygen polyhedra are dominant in the modes.