Analysis of amplitude and dissipation factor of AT-cut quartz crystal resonators over a wide temperature range

Quartz Crystal Resonators (QCR) are fundamental components of Quartz Crystal Microbalance with Dissipation Monitoring (QCM-D) sensors, which are highly sensitive to temperature. First, theoretical and finite element models of an AT-cut QCR considering temperature coupling are established. Subsequently, the effects of quartz substrate shape and thermal stress on the amplitude and dissipation factor of the resonator across a broad temperature range are analyzed by using the constructed finite element simulation model. The results indicate that the dissipation factor shows little correlation with the shape and thermal stresses across a broad range of temperature fluctuations. The amplitude decreases gradually as the temperature rises, and the circular substrate experiences a relatively smaller rate of change compared to the squared one. Additionally, thermal stresses contribute to reducing the resonator's amplitude.