An approximate analysis of waves in layered piezoelectric plates from an interdigital source transducer

This paper presents an approximate analysis for predicting the generation of elastic waves in multi-layered piezoelectric materials, when these waves are generated using interdigital transducers (IDTs). Each IDT finger is assumed to act as a source of plane (partial) waves propagating in all directions, and the condition for efficient wave generation is taken to be when the waves from adjacent pairs add in phase. The width of the IDT fingers is not explicitly taken into account and neither are the finite dimensions of the IDT. The conditions for surface or guided wave propagation between IDT transmit and receive pairs are then determined by satisfying the boundary conditions on the surfaces and at the interfaces of the substrate, using the partial waves already determined. The outer surfaces of the substrate may be either metallized or free. The model thus predicts discrete frequencies of operation of IDT devices, corresponding to the generation of surface or guided waves. No 'width' is attached to these frequencies, because of the neglect of IDT finger width and of overall IDT dimensions. Wave profiles within the piezoelectric substrate are calculated by summation of the partial waves, to depict the depth-dependence of the mechanical displacement, electric potential and energy flow. This information is used to distinguish surface waves from guided waves and to show the depth of penetration of the surface waves. The paper is essentially divided into three parts. The model formulation is presented, computational methods and associated difficulties are discussed, and sample model predictions for Rayleigh and SH wave devices in ST cut quartz are compared with experiment, showing good agreement.