Acoustoelastic analysis of thin pre-stressed films by the stiffness matrix method

Investigations using surface acoustic waves provide information on the elastic properties of thin films. The stress induced changes of the phase velocity of the surface waves are a phenomenon known as AE (acoustoelastic) effect. The stress in the thin film is assumed to be inhomogeneous due to the stress profile as a function of film thickness. For a description of the profile, the film is divided into some sublayers with gradually differing stresses. The elastic characteristics of each sublayer are obtained according to its crystallographic orientation by application of acoustoelasticity theory. The stresses are assumed to be biaxial, only the stress components σ110 and σ220 are different from zero with σ110=σ220. In order to calculate the response of the layered system in the presence of inhomogeneous stress, we extended the stiffness matrix method for the surface acoustic wave propagation in a multilayered stressed system. The method is closely related to the transfer matrix method, but it is numerically stable for high frequency and incidence angle. The generalized method is applied to the calculation of the AE effect for Love modes and Rayleigh modes propagating in the crystallographic direction [1 0 0] for a layered Ge/Si(0 0 1) system and along the [1 1 1] direction for a Ag/Si(1 1 1) system.