Inversion of Surface Acoustic Wave Data to Determine the Elastic Constants of Nitride Films

Abstract

The elastic constants of single-crystal transition-metal nitride films were determined from the inversion of surface acoustic wave (SAW) dispersion data obtained by line-focus acoustic microscopy. Measurements were carried out on the (001) plane of cubic crystal TiN and NbN films grown on cubic crystal MgO substrates. Dispersion curves of SAWs propagating along the symmetry axes, namely the [100] and [110] directions, were obtained from the wave velocities for various film thicknesses and wave frequencies. Using a modified simplex algorithm, an inversion of the SAW dispersion data yields the elastic constants of cubic symmetry, namely ell, c12, and c44. The inversion procedure essentially consists of seeking a least-square fit of the experimental data by the dispersion relation. The Rayleigh wave velocity calculated from the determined elastic constants agrees well with results measured by Brillouin scattering spectroscopy.