Properties of transducers and substrates for high frequency resonators and sensors

Abstract

Properties of transducers and substrates for bulk acoustic wave resonators and sensors are described. These resonators utilize one-dimensional thickness vibrations of structures consisting of a low-loss substrate crystal surmounted by a thin active piezoelectric film that drives the composite in resonant modes to achieve gigahertz frequencies. The structures considered include oblique orientations of the substrate, leading to generation of coupled elastic modes in the composite. A modified Christoffel-Bechmann ͑CB͒ formalism is presented to calculate acoustic wave speeds and displacements in the piezoelectric film transducer and the substrate. The CB method also yields the piezoelectric coupling coefficients of arbitrarily oriented piezofilms, for electric fields impressed either along the thickness or laterally. The calculations apply generally to transducer and substrate crystals of any symmetry class. The piezoelectric portion is then made specific for films of class 6 mm ͑wurtzite structure͒ with arbitrary orientation on the substrate, and the substrate calculations are specified for class 3m materials, but apply also to any substrate with 3m or 32 symmetry. Zinc oxide and sapphire are used in an example of the acoustic resonator structure.

Acoustic properties of piezoelectric cubic crystals

“…The cubic to be solved is $${c}^{3}-{c}^{2}\cdot [{c}_{66}^{\prime \prime}+{c}_{22}^{\prime \prime}+{c}_{44}^{\prime \prime}]+c\cdot [{c}_{66}^{\prime \prime}\cdot {c}_{22}^{\prime \prime}+{c}_{22}^{\prime \prime}\cdot {c}_{44}^{\prime \prime}+{c}_{44}^{\prime \prime}\cdot {c}_{66}^{\prime \prime}-(c{{}_{24}^{\prime \prime}}^{2}+c{{}_{46}^{\prime \prime}}^{2}+c{{}_{26}^{\prime \prime}}^{2})]-[{c}_{66}^{\prime \prime}\cdot {c}_{22}^{\prime \prime}\cdot {c}_{44}^{\prime \prime}+2\cdot {c}_{24}^{\prime \prime}\cdot {c}_{46}^{\prime \prime}\cdot {c}_{26}^{\prime \prime}-({c}_{66}^{\prime \prime}\cdot c{{}_{24}^{\prime \prime}}^{2}+{c}_{22}^{\prime \prime}\cdot c{{}_{46}^{\prime \prime}}^{2}+{c}_{44}^{\prime \prime}\cdot c{{}_{26}^{\prime \prime}}^{2})]=0$$; see Ref. [579]. Subscript m on c m specifies the wave.…”

A semi-numerical model of a lateral field excited piezoelectric fluid sensor

“…2 for both materials for lateral field excitation over a varying angle Ψ. The excitable modes which are quasiextensional, fast-and slow-quasi-shear mode are traditionally denoted by a, b, and c, respectively [16]. Here, the rotation is around the thickness axis and therefore corresponds to a rotation of the electrodes as shown in Fig.…”

On the Anomalously Strong Dependence of the Acoustic Velocity of Alumina on Temperature in Aluminosilicate Glass Optical Fibers—Part II: Acoustic Properties of Alumina and Silica Polymorphs, and Approximations of the Glassy State

“…As the packing density approaches that of pure single crystal alumina, it is presumed that the isotropic properties do as well. Table provides some salient data for α‐alumina …”