Piezoelectric characteristic length

Piezoelectric crystal resonators for frequency control and ultrasonic applications are often judged by a number of differing metrics, depending upon the intended application. Acoustic quality factor, Q, and electromechanical coupling factor, k, are two most often used. None of the usual performance figures is entirely adequate for characterizing resonators for applications at high frequencies. This paper describes various metrics traditionally applied to resonators. It tabulates observed values for each performance metric for both mature materials such as quartz and lithium niobate, as well as newer substances like langasite and thin-film aluminum nitride. An entirely new metric, with dimensions of a characteristic length is then introduced, and tabulated. It rationalizes the judging of material suitability for high frequency resonator use. The new measure is a combination of all of the physical quantities normally associated with acoustic waves in piezoelectric crystals: mass density, dielectric permittivity, piezoelectric modulus, elastic stiffness and viscosity. Use of the new performance figure leads to a number of counterintuitive conclusions regarding future directions for research, and suggests unobvious emphases for the future technology