On the existence of surface acoustic waves on piezoelectric substrates

The existence of surface waves on anisotropic materials was proven under fairly general conditions by Lothe and Barnett in 1976. But, until now, the status of surface waves on piezoelectric materials has remained unresolved. This paper presents general existence theorems for surface waves on piezoelectric substrates. It is demonstrated that for short circuit boundary conditions a surface wave solution must exist under virtually any circumstances. However, for a free surface, comparatively stringent existence conditions are required. Numerical examples are given for both free and shorted surfaces, and it is demonstrated that, in some situations, a surface wave solution may not exist for free surface propagation. The existence proofs were developed as a result of theoretical work on Green function modeling, which is now the preferred technique for rigorous SAW and pseudo-SAW device analysis. The mechanisms of the existence proofs and the associated mathematical results give great insight into the structure and properties of the Green functions and include many results that are directly relevant to device analysis.