Development of double layered thickness-shear resonator using langasite-type piezoelectric single crystal

Abstract

A novel device structure “double layered thickness-shear resonator” was proposed to improve the temperature characteristics of a bulk acoustic wave resonator. In order to design the double layered resonator, optimal combination of cut angles and thickness ratio of the substrates were determined from calculations using material constants and their temperature coefficients measured for a Ca3TaGa3Si2O14 (CTGS) single crystal. Based on the results, a double layered resonator was fabricated by directly bonding two CTGS substrates with cut angles of 122°Y and 171°Y under the thickness ratio of 0.248. As a result, the double layered resonator operated successfully at a fundamental mode of around 7.5 MHz like a normal resonator exhibiting temperature compensation effect. The mechanism of the deviation from the expected value observed in the measured temperature dependence of the frequency changes was discussed using the model of the wave propagation and the electric field generated in the double layer structure.

Development of calculation model for designing temperature characteristics of double-layered thickness-shear resonator

“…where # df 1 and # df 2 are the temperature characteristics of the resonance frequency change of the #1 layer and the #2 layer, respectively, and r is the ratio defined by relevant parameters between two substrates. At the beginning of this work, 36) the ratio r is defined as thickness ratio r h as following:…”

“…This trend was also observed in the CTGS-DLR measurements in the previous work. 36) From this fact, it can be said that Model 3 is a formula that correctly expresses the characteristics of DLRs.…”

“…Therefore, we proposed a "double layer resonator (DLR)" using a Ca 3 TaGa 3 Si 2 O 14 (CTGS) single crystal substrate and confirmed its temperature compensation effect. 36,37) We also developed a calculation model for predicting temperature characteristics using the electric flux density ratio. 37) However, the calculation results of this model were significantly different from the measured values of the temperature characteristics of the α-quartz double-layered resonator (QZ-DLR).…”

Influence of reflected waves at the bonded boundary in double-layered thickness-shear resonator using α-quartz

“…Two substrates with different cut angles are directly bonded and compensate mutual temperature characteristics of resonant frequency. At the beginning of this work, 25) the temperature characteristics of the resonance frequency for the double-layered thickness-shear resonator (df DL ) was estimated using following equation:…”

“…[18][19][20][21][22][23][24] In previous work, we confirmed the compensation of the temperature characteristics by directly bonding substrates with different cut angles with positive and negative characteristics, and also developed a prediction equation for that by considering the electric flux density ratio. 25,26) In general, when the acoustic impedance of the two substrates are different, the waves reflected at the bonded boundary are inevitably generated. However, the influence of the reflected waves could not be observed for the case of CTGS due to the small anisotropy of the acoustic impedance.…”