Infrared spectra in amorphous alumina: A combined ab initio and experimental study

We present a combined study based on the experimental measurements of an infrared (IR) dielectric function and first-principles calculations of IR spectra and the vibrational density of states (VDOS) of amorphous alumina $(\mathrm{am}\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{O}}_{3})$. In particular, we show that the main features of the imaginary part of the dielectric function ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})$ at $\ensuremath{\sim}380$ and 630 ${\mathrm{cm}}^{\ensuremath{-}1}$ are related to the motions of threefold-coordinated oxygen atoms, which are the vast majority of oxygen atoms in am-${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$. Our analysis provides an alternative point of view with respect to an earlier suggested assignment of the vibrational modes, which relates them to the stretching and bending vibrational modes of ${\mathrm{AlO}}_{n}$ ($n=4$, 5, and 6) polyhedra. Our assignment is based on the additive decomposition of the VDOS and ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})$ spectra, which shows that (i) the band at $\ensuremath{\sim}380\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ features oxygen motions occurring in a direction normal to the plane defined by the three nearest-neighbor aluminum atoms, i.e., out-of-plane motions of oxygen atoms; (ii) Al-O stretching vibrations (i.e., in-plane motions of oxygen atoms) appear at frequencies above $\ensuremath{\sim}500\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which characterize the vibrational modes underlying the band at $\ensuremath{\sim}630\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. Aluminum and fourfold-coordinated oxygen atoms contribute uniformly to the VDOS and ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})$ spectra in the frequency region $\ensuremath{\sim}350--650$ ${\mathrm{cm}}^{\ensuremath{-}1}$ without causing specific features. Our numerical results are in good agreement with the previous and presently obtained experimental data on the IR dielectric function of $\mathrm{am}\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ films. Finally, we show that the IR spectrum can be modeled successfully by assuming isotropic Born charges for aluminum atoms and fourfold-coordinated oxygen atoms, while requiring the use of three parameters, defined in a local reference frame, for the anisotropic Born charges of threefold-coordinated oxygen atoms.