Acoustoelastic effect in anisotropic layered structures

Mechanical stress alters the velocity of acoustic waves, a phenomenon known as AE (acoustoelastic) effect, which is of particular importance for the wave propagation in layered heterostructures. In order to calculate the AE effect of layered systems in the presence of stress we extended the transfer-matrix method for acoustic wave propagation by considering the change of the density, the influence of residual stress, and the modification of the elastic stiffness tensor by residual strain and by third-order constants. The generalized method is applied to the calculation of the angular dispersion of the AE effect for transverse bulk modes and surface acoustic waves on the Ge(001) crystal cut. The AE effect is found to depend significantly on the propagation direction and can even change si,on. The maximum velocity change occurs for transversally polarized waves propagating parallel to the [110] direction. For the layered Ge/Si(001) system the AE effect is investigated for Love modes propagating in the [100] and [110] directions. The AE effect increases rapidly with increasing layer thickness and reaches almost its maximum value when the wave is still penetrating into the unstressed substrate. For higher-order Love modes the increase of the AE effect is even steeper and, furthermore, can reach higher values.