Modified Butterworth-Van Dyke circuit for FBAR resonators and automated measurement system

Microwave Film Bulk Acoustic Resonators (FBARs) may be characterized by means of the Mason transmission line model, but for parameter extraction and design studies, the lumped Butterworth-Van Dyke (BVD) model is more useful. We propose a modification to the standard five element BVD model, in which a second resistor is added in series with the plate capacitance C₀. This improves the model predictions as compared to the data obtained from a network analyzer (NWA). Here, the modified model will be developed in terms of the resonant frequencies, effective coupling constant k_t² , and the quality factor Q, as determined from the S parameters of an FBAR measured by the NWA. To evaluate the FBAR resonators on a routine basis, an automated data acquisition and parameter extraction method based on the Modified Butterworth-Van Dyke model (MBVD) is described. An Agilent Technologies 8753ES NWA operating under Personal Computer control is used to acquire and process FBAR data by means of a custom HPVEE^TM program, which transfers data from the NWA, and extracts the six MBVD circuit parameters. Excellent agreement is obtained between the measured data for a typical FBAR resonator and calculated “postdictions” obtained from the MBVD circuit. Coupled with the automated method, which takes about 10 seconds per resonator to perform a complete extraction cycle, a computer controlled probing station is used to acquire data from several hundred resonators on the wafer upon which the FBARS were fabricated. With this speed and probing capability, it is feasible to wafer map the FBARs for uniformity. Contour plots of the measured resonant frequency and coupling constant k_t² will be presented to illustrate the capability