Out of the plane curling effect in MEMS cantilever beam

Out of plane curling of the cantilever beam and its bending directions has remained a trivial issue in MEMS technology. Out of plane curling of the cantilever beam occurs during fabrication due to the residual stress or stress gradient in the beam material. This poses difficulty in obtaining its deflection as well as resonance frequency. While we have fabricated Silicon dioxide cantilever, we had a challenging task to measure the deflection of curled cantilever beam and its resonance frequency. Even though there are numerous materials and modeling methods available to compensate the curling effects by additive material(s), these methods advocate stress relief than living with it. This work presents the development of an analytical model for a MEMS cantilever beam determining the shift in designed resonant frequency of curled cantilever beam due to surface stress since silicon dioxide is in compression. The shift in resonant frequency of the uncurled cantilever beam is different from the shift in curled beam. We have focused on understanding physics of the curled beam to get the resonant frequency back to its designed value. Our analytical model is based on its lumped parameter behavioral model in mechanical domain. Partial results have been obtained to study the parametric behavior of curled cantilever beam.