Lagrangian model of the frequency-temperature behavior of SAW resonators

Abstract

The experimental studies of temperature coefficient of frequency (TCF) of SAW resonators were usually modeled by TCF models first proposed by Bechmann, Ballato and Lukaszeck[1]. These models unfortunately were not frame invariant with regards to the material property tensors of the crystal substrate and metal interdigital transducers (IDTs). Furthermore the models did not have the 3rd order nonlinear elastic constants that were needed to account for the effects of thermal strains from mountings, boundary constraints, and material interfaces. We employed a Lagrangian model of TCF of SAW resonators wherein governing equations for incremental vibrations superposed on thermal strains were implemented in a finite element program. The model used material coordinates referred to a fixed reference frame at a reference temperature, therefore the material property tensors were frame invariant. In addition it had a term that was a product of the 3rd order nonlinear elastic constants and thermoelastic strains. This product could account for the thermoelastic strains from interfacial stresses and boundary conditions. The objective of our study was to provide an accurate and detailed finite element model of the effects of the crystal substrate, metal IDTs, and stack layers on the TCF of SAW resonators. Good comparisons of model results with the experimental results were found for the 1 GHz lithium tantalate YXl 42° shear horizontal SAW resonator. Characterization of the electrode film properties was found to be important, especially when the film thickness was increased from 2000 A to 4000 A.