Optimizing UHF quartz MEMs resonators for high thermal stability

A 1 GHz AT-cut quartz thickness shear mode resonator is modeled for the first time with thermally induced bonding stresses and their effect on the device frequency-temperature (f-T) characteristic. Without the details of the bonding configuration, modeling indicates the f-T characteristic slightly rotates as a function of the change in stiffness of a simplified absorbing mount. However, if details of the bonding configuration are included, our modeling predicts the potential for a significant distortion in the f-T curve. High or varying stress over temperature in the device active region is found to lead to an undesirable increase in the f-T slope. The origin of the active region stress can be varied, but in practice it frequently originates from a temperature dependent bonding stress, or from fabrication steps such as metal depositions. In this paper we highlight the magnitude of the thermal stress effect on the f-T curve, and offer design methods that mitigate the thermally induced bonding stress by de-coupling the active resonator area from high stress regions of the quartz device.