Acoustoelastic effect in stressed heterostructures.

Mechanical stresses influence the phase velocity of acoustic waves, known as the AE (acoustoelastic) effect. In order to calculate the AE effect of biaxially stressed layered systems, 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 Ge(001). Our calculations reveal that the AE effect significantly depends on the propagation direction and can even change sign. The maximal 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 almost reaches its maximal value when the wave still penetrates into the unstressed substrate.