Vibrational properties of AlN grown on (111)-oriented silicon

We study the vibrational spectrum of AlN grown on Si(111). The AlN was deposited using gas-source molecular beam epitaxy. Raman backscattering along the growth c axis and from a cleaved surface perpendicular to the wurtzite c direction allows us to determine the ${E}_{2}^{1},$ ${E}_{2}^{2},$ ${A}_{1}(\mathrm{TO}),$ ${A}_{1}(\mathrm{LO}),$ and ${E}_{1}(\mathrm{TO})$ phonon energies. For a 0.8-\ensuremath{\mu}m-thick AlN layer under a biaxial tensile stress of 0.6 GPa, these are 249.0, 653.6, 607.3, 884.5, and 666.5 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, respectively. By combining the Raman and x-ray diffraction studies, the Raman stress factor of AlN is found to be $\ensuremath{-}6.3\ifmmode\pm\else\textpm\fi{}1.4{\mathrm{cm}}^{\ensuremath{-}1}/\mathrm{GPa}$ for the ${E}_{2}^{2}$ phonon. This factor depends on published values of the elastic constants of AlN, as discussed in the text. The zero-stress ${E}_{2}^{2}$ energy is determined to be $657.4\ifmmode\pm\else\textpm\fi{}0.2{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}.$ Fourier-transform infrared reflectance and absorption techniques allow us to measure the ${E}_{1}(\mathrm{TO})$ and ${A}_{1}(\mathrm{LO})$ phonon energies. The film thickness (from 0.06 to 1.0 \ensuremath{\mu}m) results in great differences in the reflectance spectra, which are well described by a model using damped Lorentzian oscillators taking into account the crystal anisotropy and the film thickness.