The paper presents a study of surface acoustic waves propagation in a damage layer with finite thickness and residual stress on an orthotropic semi-infinite medium to reveal the application of laser ultrasound in the surface inspection of ground silicon wafers. Biot’s theory of small deformations influenced by initial stress forms the basis for this study. Considering the case that the displacement and boundary forces are continuous at the interface and the forces vanish on the free surface, the required dispersion relation is obtained. We consider a sample of (1 0 0) silicon wafer by grinding with fine abrasive grains, which has a machined face with a micrometer-level thickness of surface damage and residual stress. In order to discuss the impact of propagation directions, degree of surface damage, residual compressive stress on the velocity characteristics of surface waves, the numerical computation of the dispersion equations is performed. It has been found that surface damage has a significant effect on the dispersion curve, while the residual compressive stress can only cause a small decrease Δc in the surface wave velocity. The velocity decrease Δc becomes obvious at high frequencies. For a fixed residual compressive stress and frequency, Δc hardly changes with the degree of surface damage and propagation directions. Based on the above characteristics, we study the inverse problem on detecting both surface damage and residual stress simultaneously by SAW velocities and give a corresponding iterative algorithm. This study may provide theoretical guidance for non-destructive testing of residual stress.

本文对正交各向异性半无限介质上具有有限厚度和残余应力的损伤层中的表面声波传播进行了研究，以揭示激光超声在地面硅晶片表面检测中的应用。毕奥特的受初始应力影响的小变形理论为该研究奠定了基础。考虑到位移和边界力在界面处连续并且力在自由表面上消失的情况，获得了所需的色散关系。我们考虑（1  0 0）通过用细磨粒研磨的硅片，其加工面的表面损伤和残余应力为微米级厚度。为了讨论传播方向，表面损伤程度，残余压应力对表面波速度特征的影响，进行了色散方程的数值计算。业已发现，表面损伤具有分散曲线上的显著影响，而残留压缩应力只会导致小的下降Δ Ç在表面波速度。速度降低Δ Ç变成在高频时明显。对于一个固定的残余压应力和频率，Δ Ç几乎不随表面损伤程度和传播方向而变化。基于上述特征，我们研究了利用声表面波速度同时检测表面损伤和残余应力的反问题，并给出了相应的迭代算法。这项研究可以为残余应力的无损检测提供理论指导。