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In this paper, we utilize a phonon detection technique to determine the temperature coefficient of resonant frequency TC f of MEMS resonators. The technique adopted is highly sensitive to device motions and allows for TC f measurement with less than 5 ppm • C −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 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 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 f of the devices by up to 22%. From our TC 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 −8 • C −1 for one particular sample die.

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This paper presents a comprehensive study of the nonlinearities in micromechanical clamped-clamped beam resonators using a stroboscopic scanning electron microscopy (SEM) technique. Stroboscopic SEM allows direct imaging and measurement of the resonator's momentary displacement, hence eliminating the uncertainties associated with the conventional characterization methods. Five different silicon-on-insulator (SOI) comb-drive clamped-clamped beam resonators with resonant frequencies ranging from 113 kHz to 239 kHz were designed, fabricated and tested to investigate how their nonlinearities are related to the device dimensions. Both the theoretical analysis and experimental results conclusively show that the critical vibration amplitude of the resonator is around 1% of the beam width in a vacuum and is relatively independent of the beam length. Furthermore, it is found that the maximum storable energy of the resonator can be significantly increased by increasing the beam width and/or reducing the beam length if there are no restrictions on these dimensions. On the other hand, if a specific resonant frequency needs to be maintained, the maximum storable energy can be improved by increasing both the beam width and length by the same factor. Such a study not only helps to reveal the intrinsic nonlinear properties of the micromechanical clamped-clamped beam resonators, but also provides useful design guidelines for engineers to optimize the overall device performance.

In this work, three useful techniques for dynamic motion characterization of MEMS devices are presented, namely network analyzer, acoustic phonon detection and stroboscopic SEM techniques. Proof-of-concept experiments using an MEMS electrostatic resonator reveal reliable and consistent measurement results from the three techniques. The network analyzer characterization technique is most widely used in practice due to its convenience, high sensitivity and high speed. The second acoustic phonon technique features non-invasive and package level testing, but it is still an indirect characterization method, like the network analyzer. In acoustic phonon detection, mechanical waves (phonons) generated by the actuated MEMS device are used as the coupling mechanism through which information on the dynamic mechanical state of the device can be obtained. The third stroboscopic SEM technique is capable of directly measuring the device motion, but its throughput is low and hence not suitable for high volume testing. The stroboscopic SEM imaging system is based on time-gated sampling of the analogue secondary electron (SE) signal. Unlike conventional SEM, stroboscopic SEM is able to detect the actual position of the structure at a specific point in time by taking a time-gated sample of the SEM SE signal at a specific phase of the structure's motion.