Dynamic Analysis of Multi-Beam MEMS Structures for the Extraction of the Stress-Strain Response of Thin Films

Freestanding MEMS structures made of two long connected beams from different materials are fabricated and released in order to extract the stress-strain properties of thin films. The first material, named actuator, contains a high internal tensile stress component and, when released, pulls on the other beam. The strain in the beams is calculated based on the measurement of the displacement with respect to the reference configuration using scanning electron microscopy. The stress is estimated using two different methods. The first method, already reported, is based on the displacement of the actuator and the knowledge of its internal stress. The method which constitutes the novelty of the present study is based on the dynamic analysis of the multi-beam structures, and the determination of the stress value that corresponds to the measured resonance frequencies. The dynamic analysis is performed via two different methods: (i) the modified Rayleigh–Ritz technique and (ii) the Euler–Bernoulli beam dynamics. Results are provided for palladium thin films which deform plastically and for monocrystalline silicon thin films, exhibiting a purely elastic behavior. The results show the higher accuracy of the dynamic measurements for the estimation of the stress compared to the static method. The dynamic measurements also show that the Rayleigh–Ritz technique tends to give a higher bound for the resonance frequencies compared to the Euler–Bernoulli technique. This dynamic method extends the potential of this on-chip material testing technique which can also be adapted to stress controlled sensors applications.