Frequency temperature behavior of bi-mesa shaped at cut quartz resonators

To confirm the effect of bi-mesa structures on the decoupling of thickness-shear (TS) and thickness-flexure (TF) modes, we measured the frequency-temperature behavior of bi-mesa shaped AT cut quartz resonators. The TF mode couples with the TS mode because the same displacement component is contained within the TS mode. This strong coupling cannot be eliminated as long as the plates have boundaries. Therefore, the temperature characteristics of the fundamental TS mode are clearly affected by the TF components. Bi-mesa structures have an energy trapping effect large enough to spatially separate the vibrational modes, so bi-mesa structures can decrease the effect of TF components. Therefore, the frequency-temperature behavior of a bi-mesa resonator is close to that of an infinite plate, which has no TF component effect. The bi-mesa resonators used in this study were fabricated using a wet etching process, and the fundamental TS frequency was 8.3 MHz. The frequency-temperature behavior was measured using a network analyzer. Results showed that bi-mesa resonators have temperature characteristics four times better than those of flat resonators, ranging from -20 to 85/spl deg/C. These results confirm the energy trapping effect of bi-mesa structures and their effectiveness in separating vibrational modes.