Theory of elastic wave propagation in anisotropic film on anisotropic substrate: TiN film on single-crystal Si

The delta-function representation of the elastodynamic Green's function is used to derive an expression for the elastic wave forms on the surface of an anisotropic thin film on an anisotropic substrate due to a point or a line source located at the surface of the film. The dispersion relation for surface acoustic waves (SAWs) is obtained from the poles of the Green's function. A computationally efficient algorithm is formulated to obtain the elastic constants and the density of the film from the SAW dispersion data. The theory is used to analyze measured SAW dispersion relations in a titanium nitride film on silicon. The analysis yields values of the elastic constants and the density of the film. Excellent agreement is obtained between the theoretical and experimental dispersion results. Calculated wave forms for the surface wave due to a pulsed line source on the surface of the film are reported.