Non-uniform distribution of motion influence on the effective mass-loading in AT-cut quartz resonators

Comparative study of the mass-loading effect on electrical parameters of gallium phosphate, quartz and langasite resonators

“…The experimental results for AT-cut quartz resonators [11,12] were in good agreement with the theory From these results one can conclude that the non-uniform distribution of motion depending on electrode geometry could be ascribed to the coupling of the thickness-shear and thickness-twist modes and to the effects associated to the electrode deposition. The resonance and anti-resonance frequencies and series resistances of the fundamental, 3 rd , 5 th and 7 th overtones of the plates with and without electrodes were measured after each electrode layer deposition.…”

“…These observations, compared to the previous experimental and theoretical results [11,12,13], allow to assign the increase of the inductance with order of overtone to the decrease of the active area of AT-cut quartz resonators due to the non-uniform distribution of motion under electrodes. On the other side the non-uniform distribution of motion is partially determined by stresses at interface electrode-piezoelectric substrate.…”

“…Based on our previous results [11,12] according to which the inductance change with mass-loading is due to the internal stress at interface electrode-piezoelectric substrate, we could ascribe the specific behavior of inductance of Y-cut langasite, and AT-cut gallium phosphate to a much smaller interfacial stresses in comparison with AT-cut quartz resonators.…”

“…Based on the experimental results obtained in [11,12] the non-uniform distribution of motion could be ascribed to the effects associated to the electrode deposition at the interface electrode-piezoelectric substrate including defects and stresses.…”

Investigations on the langasite resonators by X-ray topography

“…The theoretical and experimental investigations of massloading effect on thickness-shear AT-cut, SC-cut quartz resonators and Y-cut langasite resonators, using the Ballato's transmission-line analogs [1], have shown that the harmonic dependence of electrical parameters is influenced by the electrodes [2,3]. The studies are based on the assumption of non-uniformity of the vibratory motion over the electrode area of the crystal, due to the coupling of the thickness-shear with thickness-twist modes of vibration and to the stresses at interface electrode-piezoelectric plate.…”