Estimating residual stress, curvature and boundary compliance of doubly clamped MEMS from their vibration response

Structural parameters of doubly clamped microfabricated beams such as initial curvature, boundary compliance, thickness and mean residual stress are often critical to the performance of microelectromechanical systems (MEMS) and need to be estimated as a part of quality control of the microfabrication process. However, these parameters couple and influence many metrics of device response and thus are very difficult to disentangle and estimate using conventional methods such as the M-test, static mechanical tests, pull-in measurements or dynamic mechanical tests. Here we present a simple, non-destructive experimental method to extract these parameters based on the non-contact measurement of the natural frequencies of the lowest few eigenmodes of the microfabricated beam, and knowledge of Young's modulus and plan dimensions of the beam alone. The method exploits the fact that certain eigenmodes are insensitive to some of these structural parameters which enable a convenient decoupling and estimation of the parameters. As a result, the method does not require complicated finite element analysis, is insensitive to the gap height and introduces no contact wear or dielectric charging effects. Experiments are performed using laser Doppler vibrometry to measure the natural frequencies of doubly clamped, nickel, RF-MEMS capacitive switches and the method is applied to extract the residual stress, beam thickness, boundary compliance and post-release curvature.