Design of a quartz microresonator for infrared sensor applications

A quartz crystal resonator's resonance frequency is sensitive to temperature, and a quartz thermometer can accurately detect temperature changes of microkelvins. Making the resonator in a microscopic scale increases its temperature detectivity as well as enables a large array for an IR sensor. Incoming radiation energy of such an IR sensor needs to be absorbed in the resonator as much as possible, and this requires a different geometry of the electrodes from those of a conventional resonator; e.g., a ring electrode on the IR illumination side and a solid electrode on the other side. The geometry of these electrodes should be optimized in order to obtain a maximum energy trapping, which maximizes the value of Q and minimizes the resonator noise, resulting in maximizing the detectivity. Analytical and numerical solutions of the approximate scalar differential equation of Stevens and Tiersten describing the transverse behavior of essentially thickness modes are obtained for a rectangular resonator with a ring electrode on one side and a solid electrode on the other side. These solutions are used to study the performance of this electrode geometry and a general design is presented.