Exploring One-dimensional Micromechanical Resonators with Residual Stresses for Potential Sensing Applications and Measurement of Mechanical Properties
Recently the domain of microelectromechanical systems (MEMS) has seen an unprecedented rise in use of varieties of new materials other than the conventional silicon and related materials originally borrowed from semiconductor manufacturing processes. This material-diversity, combined with several different deposition processes for thin films gives rise to a wide range of material properties. The gradual shift offers numerous opportunities in the form of increased functionalities for sensing applications with device footprint remaining unchanged. At the same time, it brings the challenges of finding material properties, which is essential for predictive design. We are interested in both of these frontiers, and our approach towards accomplishing the next leap in this field of technology is two-pronged. We want to explore the novel transduction mechanisms that might open-up new fields of sensing applications. In parallel, we wish to enable new techniques for the measurement of material properties. In this work, we have studied the effect of residual stress on dynamic characteristics of microscale fixed-fixed beams with more emphasis on the post-buckled regime. We find that only the frequencies of odd-order modes (first and third) vary with change in compressive axial load, whereas the even-order modes (second and fourth) remain invariant. Based on these observations, we show that it is feasible to use the odd-order modes for sensing applications and even-order modes for applications requiring frequency stability of resonators. Although theoretically it is known that the second mode cannot be excited directly with any uniform excitation, we experimentally show that it is feasible to repeatably excite the second mode in a fixed-fixed micro-beam around its first-buckled state when subjected to uniform base excitations. We verify that this excitation is not a result of coupling with the first mode, the commonly known cause. The measured frequency response shows that the second mode is directly excited, possibly due to presence of structural imperfections. The interesting dynamic behaviour observed in the buckled beams makes them a novel platform for study of nonlinear phenomenon. We have deposited a thin layer of metal on the buckled-beams, and by applying an appropriate voltage to this metal layer, we alter their state of stress. We have measured the natural frequencies of the beam at each applied voltage and studied how the frequencies evolve with change in the resulting residual stress. Further, we have used the phenomenon of invariance of even mode frequencies with respect to axial stress variation in buckled beams to decouple the effect of stress and modulus on a beam’s frequency response. We leverage this behaviour for simultaneous estimation of Young’s modulus and residual stress of released micromechanical structures. The occurrence of over-etching during release of devices poses a challenge for accurate determination of length. We have addressed this issue by considering length as an unknown parameter in the model, and by using multi-parameter fitting, we are able to estimate the effective under-etched length. Three different procedures are proposed for the measurement of Young’s modulus, residual stress, and effective length. Using the proposed methods, residual stress is estimated in amorphous silicon carbide thin films (SiCx) deposited by PECVD and reactive sputtering. Besides, modulus values of four materials (PECVD SiNx, PECVD SiCx, sputtered SiCx, and silicon) is estimated and compared with the reported results.