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

Abstract

The influence of the reflected waves at the bonding boundary on the resonance waveform and temperature characteristics was investigated using α-quartz (QZ). The double-layered resonator specimen was fabricated using 129.55°Y- and 0°Y-cut QZ substrates with the thickness ratio x=0.520. The temperature characteristic at the range from 100°C to 300°C was deviated from the calculated values estimated by the equations considering thickness and electric flux density ratio proposed in the previous work, and the resonant waveform of the specimen was deteriorated as compared with that of single-layer resonators. In order to clarify these phenomena, the phase matching conditions and total amplitude in the specimen were examined. As a result, it was clarified that increase of the amplitude in the layer with lower acoustic impedance was affected to the temperature characteristic, and acoustic losses due to reflection / transmission at the bonding boundary was affected to the total amplitude of resonance.

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

“…However, in Model 2, the predicted values of the temperature characteristics of α-quartz DLR were significantly different from the experimental values. 38) Therefore, we propose a new calculation model as "Model 3" as shown below. In Model 3, the ratio r is defined as total strain ratio r S considering the influence of the waves reflected at the bonding boundary as follows:…”

“…Using Model 3, we will try to calculate the temperature characteristics of α-quartz (QZ) DLR. As in the previous paper, 38) 129.55°Y-cut was selected as the #1 layer and 03SP28-3…”

“…For details regarding the specimen, please refer to Ref. 38. Since we are considering a thickness-shear mode resonator, the phase velocity used in the calculation is that of the X-axis polarized shear wave propagating in the substrate thickness direction.…”

“…The loss factors in Table I were set as the values at which the FEM resonance waveform was close to the experimental one for each single-layer resonator. 38) In this FEM analysis, the voltage applied to the electrodes was 1 V. Figure 9(a) is the grid model used in FEM analysis, and Fig. 9(b) is the cross-sectional particle displacement for the 1st mode at the center part of the QZ-DLR indicating by red dashed line in Fig.…”

“…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). 38) Based on this result, in the previous work, we proposed a calculation model using the total strain ratio that takes into account the influence of reflected waves at the bonding boundary of the QZ-DLR. 39) We found that the calculated values of this proposed model agreed well with the experimental values of the temperature characteristics for the 1st mode of the QZ-DLR.…”