Acoustoelastic effect in stressed heterostructures

Abstract

Mechanical stresses influence the phase ve- locity of acoustic waves, known as AE (acoustoelastic) effect. In order to calculate the AE effect of biaxially stressed layered systems we extended the transfer ma- trix method for acoustic wave propagation by consid- ering the change of the density, the influence of resid- ual 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 is signifi- cantly depended on the propagation direction and can even change sign. The maximum velocity change oc- curs for transversally polarized waves propagating par- allel to the (110) direction. For the layered Ge/Si(001) system the AE effect is investigated for Love modes propagating in the (loo) 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.