An Experimental Study of Residual Stress Induced Modulation of Vibration Characteristics in 1-D MEMS Resonators

We experimentally study test structures of more than 100 microelectromechanical systems (MEMS) beam resonators with clamped ends and residual stresses varying from highly tensile to compressive loads beyond buckling and provide experimental verification of some key theoretical results reported in the literature. We compare the theoretically predicted natural frequencies over a large range of residual stresses that make the one-dimensional micro-mechanical resonators behave like beams or strings, depending on the relative magnitude of the effective axial load and the flexural stiffness. In particular, we measure the natural frequencies of the first four modes of buckled beams to show the drastically different behavior of beams under post critical buckling load from those under tension and, for the first time, present experimental evidence of invariance of even modes to compressive residual stresses in microscale beams. We then derive the sensitivity of these modes to residual stresses and discuss the consequences of such sensitivity on sensing applications along with recommendations on how to engineer the required level of residual stresses.