Phonon detection technique for the study of the temperature coefficient of resonance frequency in clamped-clamped beam resonators

摘要

In this paper, we utilize a phonon detection technique to determine the temperature coefficient of resonant frequency TC{sub}f of MEMS resonators. The technique adopted is highly sensitive to device motions and allows for TC{sub}f measurement with less than 5 ppm ℃{sup}(-1) error. In addition, it can also characterize multiple resonators fabricated on the same die or wafer using a single piezoelectric element. Although the multiple devices have to be measured sequentially, the data acquisition time per resonator is short, making the technique an ideal wafer level characterization tool for high volume device testing. The devices used in our TC{sub}f experiments are comb-actuated clamped-clamped beam resonators fabricated using the SOIMUMPs process from MEMSCAP. The clamped-clamped architecture of these devices makes them especially prone to thermal-induced strain. A theoretical framework for analyzing the TC{sub}f of these resonators was also derived. Experiments on 16 sample devices show that altering the length L and width w of the clamped-clamped beam improves the TC{sub}f of the devices by up to 22%. From our TC{sub}f measurements, it was also deduced that a mismatch in the thermal expansion coefficients of the SOI structural and substrate layers caused the thermal-induced strain on our samples. The mismatch was determined to be 3.8×10{sup}(-8) ℃(-1) for one particular sample die.