Nonlinear SAW propagation in thin-film systems with residual stress,
R. E. Kumon (National Institute of Standards and Technology, Mail Stop 853, Boulder, CO 80305-3328).
Thin-film deposition often creates residual stresses that change the film's effective mechanical properties and hence affect its performance in a product. In particular, the acoustoelastic effect causes the surface acoustic wave (SAW) velocity dispersion to change, although even stresses of several GPa typically cause shifts that are only a fraction of a percent. To determine whether finite-amplitude SAWs could be used to provide additional information about residual stress in such systems, a study of SAW propagation is performed in systems with weak, strong, loading, and stiffening dispersion. The systems are assumed to have plane, equibiaxial stresses, films that are thin as compared to the wavelengths of the dominant harmonics, and harmonic generation only in the substrate. The dispersion relations are computed using a Green's function method. The harmonic generation is modeled using spectral evolution equations that account for nonlinear effects up to quadratic strain terms in the stress-strain relation. As an example, results are presented for an initially monofrequency, plane wave traveling in the  direction of systems composed of 5 to 500 nm Ge films under compressive stress of 1 GPa on an unstressed, (001) Si substrate. In the case of weak dispersion, the vertical velocity waveforms distort asymmetrically from their initial sinusoidal form and impulse shedding occurs after the largest peak. However, the residual stress has relatively little effect on the harmonic generation as compared to the unstressed case. In the case of strong dispersion, most of the energy of the wave is confined to the first few harmonics, which exhibit periodic growth and decay cycles across the surface. The residual stress causes the extrema of the harmonic magnitudes to shift location in space by approximately one percent for each characteristic nonlinear length scale traversed. [This work was performed while the author held a National Research Council Research Associateship Award at the National Institute of Standards and Technology.]