Influence of Tolerances on Acoustic Bulk Wave Resonators Made of Thin At-Cut Quartz Crystals

摘要

This work deals with the influence of tolerances on the properties of piezoelectric resonators made of crystalline quartz. At least a qualitative knowledge of these effects is needed in the design and fabrication of high quality crystal resonators, because even minor deviations from the ideal symmetry of the chosen geometry profoundly affect the mode spectrum and the coupling between modes. The analysis starts from the limitations of a typical fabrication process. The process parameters have been ordered as to their importance and the effect of their tolerances is discussed. The energy trapping principle is used to deduce the existence of an optimum plateback. The effect of tapers of both the crystal and the electrodes on the main thickness modes are discussed. The theory of the thickness-twist vibrations of the tapered resonator based on a power series expansion in the thickness coordinate (the two-dimensional MINDLIN-theory) is extended to a crystal resonator with parallel surfaces and tapered partial electrodes.