ACCURATE ELECTRICAL MEASUREMENTS OF MODERN FERROELECTRICS

Future uses of modem ferroelectrics include thin-film resonant microstructures for timing, sensing, and actuation. The frequency range of interest extends from nearly DC through the UHF band. At high frequencies especially, it is difficult to obtain precise material parameters from broadband electrical measurements. We have developed highly accurate lumped equivalent networks for these frequencies, for the two canonical cases of thickness- and lateral-field excitation. Measurements on these circuits permit extraction of the complex dielectric, piezoelectric, and elastic parameters of the material. In this paper we discuss both traditional and modern electrical network descriptions of piezoelectric resonators; we also treat how they are modified by the conditions of excitation and inclusion of loss mechanisms. The more general networks are then specialized to yield lumped circuit versions tailored to the particular attributes of ferroelectrics: high coupling and moderate loss. A numerical example is worked by means of illustration.