The use of a variationnal perturbation method combined with finite element analysis is presented here to simulate the influence of mass-loading effects on the resonance frequency of bulk acoustic wave resonator. Computations are conducted on 2D and 3D and any shape of resonator can be considered. Predictions are compared to experimental data.

This paper presents the results of the vibration modes measurements by X-ray topography in SC-cut quartz and Y-cut unpolished langasite resonators. A comparison of these results with X-ray diffraction topography images on AT-cut quartz resonators and Y-cut polished langasite resonators pointed out the behavior of mass-loading effect with plate orientation angle and with the surface state of the piezoelectric substrate. The results of the X-ray topography investigations are compared with electrical measurements performed on the same resonators. 5MHz Sawyer, plan parallel SC-cut quartz and Y-cut unpolished langasite resonators, with 14mm plate diameter and various electrode thickness and diameters have been investigated by Xray topography on fundamental, third and fifth overtones. The measurements were performed by conventional transmission Laue setting using white beam synchrotron radiation at LURE/DCI, Orsay, France. The study by X-ray topography on SC-cut quartz resonators and unpolished Y-cut langasite resonators pointed out a good agreement with the results obtained on the same resonators by electrical measurements. The conclusion is that the SC-cut quartz resonator characteristics present a similarly harmonic dependence with those of the Y-cut langasite resonators thus revealing the stress-compensated feature of the Y-cut in langasite crystal.

This paper presents the results of the X-ray topography investigations of mass-loading influence on electrical parameters of AT-cut quartz resonators and Y-cut langasite resonators. This study reveals that the mass-loading effect on electrical parameters of Y-cut langasite resonators is smaller than in the case of AT-cut quartz resonators. The results of the X-ray topography investigations are in good agreement with electrical measurements.

In this paper the results of electrical measurements of the mass-loading influence on Y-cut langasite resonator parameters are compared with those obtained by X-ray topography analysis of the same resonators. Based on the Ballato's transmission-line analogs of the trapped-energy ;resonators vibrating in thickness-shear mode [1], the mass-loading effect on resonator characteristics was studied. The effective mass-loading, motional inductance and quality factor of langasite resonators were computed. Sawyer plan-parallel polished Y-cut langasite resonators with 14mm diameter, 5 MHz resonant frequency, Au electrodes of 7 mm diameters and various thickness were used in experiments. X-ray topography measurements were performed by conventional transmission Laue setting using the white beam synchrotron radiation on fundamental, third and fifth overtones. The results are in agreement with those obtained by electrical measurements. The comparison of X-ray diffraction topography images previously performed on AT-cut quartz resonators with X-ray topographs on langasite resonators pointed out that the Y-cut langasite resonators are less influenced by the mass-loading than the AT-cut quartz resonators.