A new in situ residual stress measurement method for a MEMS thin fixed-fixed beam structure

A new method is described to measure the in situ residual stress state in a thin fixed-fixed beam structure used in microelectromechanical systems (MEMS). The methodology can be applied to devices at the anticipated operational and environmental temperatures. The new technique makes use of differences in the thermal expansion coefficient between the thin beam and the substrate. The residual stress distribution is determined by matching the thermal deflections from a finite element model (FEM) to measured deflections of the beam. All previous residual stress measurement methods for MEMS suspended structures reported a uniformly distributed residual stress. Experimental data coupled with the new analytical method suggests that this may not be adequate for the case of a suspended thin structure with nonplanar surface topology. A stress gradient through the thickness must be included in the determination of the stress state of the beam. The new method indicates a spatially varying residual stress distribution and is capable of de-coupling the mean stress and the stress gradient through the thickness. It was found through an extensive literature review that the quantification of the stress gradient in a thin suspended structure has never been reported. The de-coupling makes the prediction of the stress state at different temperature points possible. Details of the new method are demonstrated and discussed by the use of a capacitive radio frequency (RF) MEMS switch.