Acoustic properties of piezoelectric cubic crystals

Abstract

This paper is offered as a complementary adjunct to the many treatments of the electronic and photonic properties of cubic III–V and II–VI compounds appearing in the literature. These crystals typically exhibit piezoelectricity, due to the molecular dissymmetry, thereby allowing the inclusion of classical mechanical/acoustic features along with the quantum. We discuss the history of this modality and then illustrate its use by applying it to an electro-elastic problem that has the estimable virtues of having an exact solution, along with wide practical applicability: determination of the piezocoupling values governing the excitation of thickness vibrations in thin cubic films or plates of arbitrary crystallographic orientation by electric fields directed either along, or lateral to, the thickness. Explicit results are given for orientations along the great-circle paths connecting the principal directions [100], [110], and [111]. The formalism is then applied to GaAs as an example; it is further demonstrated that various results, such as the orientational variations of piezocoupling factors, are generally applicable to other members of the III–V and II–VI families by scaling. Ancillary aspects, such as errors due to misorientations, nonlinearities, and equivalent circuit representations, are described and discussed. This work is dedicated to Gerald W. Farnell (1925–2015), Prof. Emeritus, McGill University, Montréal, Canada.