Temperature measurement and compensation based on two vibrating modes of a bulk acoustic mode microresonator

A method to detect the temperature of a micromechanical resonator by measuring the frequency- shifts of two different eigenmodes is presented. The resonator is a square-extensional bulk-acoustic-resonator with two fundamental modes of vibration. The modes feature different temperature coefficients of the frequency and therefore by measuring the frequency change of both modes of vibration the temperature information can be deduced. The measured temperature is used to mathematically compensate for the temperature induced drift of the second eigenmode. The advantage of the demonstrated in-situ temperature measurement is that as no external temperature sensor is needed, the resonator temperature is accurately measured and hysteresis arising from different temperature time constants for heating and cooling of the sensor and resonator is eliminated.