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 $E_2^1,$ $E_2^2,$ $A_1\mathrm{}\left(\mathrm{TO}\right)\mathrm{},$ $A_1\mathrm{}\left(\mathrm{LO}\right)\mathrm{},$ and $E_1\mathrm{}\left(\mathrm{TO}\right)\mathrm{}$ phonon energies. For a 0.8-μm-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 ${\mathrm{cm}}^{\mathrm{-}1}$, respectively. By combining the Raman and x-ray diffraction studies, the Raman stress factor of AlN is found to be $-6.3\pm 1.4{\mathrm{cm}}^{-1}/\mathrm{GPa}$ 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 $657.4\pm 0.2{\mathrm{cm}}^{\mathrm{-}1}.$ Fourier-transform infrared reflectance and absorption techniques allow us to measure the $E_1\mathrm{}\left(\mathrm{TO}\right)\mathrm{}$ and $A_1\mathrm{}\left(\mathrm{LO}\right)\mathrm{}$ phonon energies. The film thickness (from 0.06 to 1.0 μm) 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.