Monolithic integration of AT-cut resonators using artificial twin quartz plate

The monolithic integration of AT-cut quartz resonator arrays was investigated. To reduce the mechanical coupling between resonators formed on an AT-cut quartz plate, an x-axis inversion area was formed between the resonators. As the cutoff frequency of thickness shear wave in the x-axis inversion area is much higher than that for the AT-cut area, the thickness shear wave excited in the AT-cut area decays rapidly in the x-axis inversion area. The attenuation constant, α, of thickness shear wave in the x-axis inversion area is approximately given by α=23.2W/H [dB], where W and H are respectively the width of the x-axis inversion area and plate thickness. When the width W is 3H, the attenuation is about 70 dB. Therefore, almost complete separation between AT-cut resonators is obtained with very short width of the x-axis inversion area. Many resonators without mechanical coupling can be formed monolithically by the use of a lattice shaped x-axis inversion area