Shape effect on mechanical quality factor of micro-resonator

The effect of shape on the mechanical quality factor, Q, of a micromachined cantilever resonator has been investigated with a focus on the energy loss in the resonator, which is due to the internal friction of moving parts. Theoretical modeling and numerical simulations based on FEM were performed on a test structure. The relative value of Q was calculated by summing the squares of the stress on each constituent element of the beam when the curvature of either the support base or the resonating beam was varied. Test structures were fabricated and the mechanical quality factor was measured. The theoretical and experimental results agree well, which shows that stress distribution is an important factor determining Q. It was found that the curvature of the supporting base has little effect on Q, but that the curvature of the beam has a considerable effect.