A model for piezoresistance in torsional MEMS springs

A piezoresistive readout method for MEMS torsional resonators is presented. To this purpose, a new theoretical model describing the piezoresistive effects on monocrystalline and polycrystalline beams, used as suspended resistors, is investigated. A square law, linking the angular displacement thetas to the resistance variation DeltaR, is derived. The theory is confirmed by ANSYS FE (finite element) simulations. When adding a feedback to an actuator, a piezoresistive sensing part can read the output signal without increasing the process complexity and represents an alternative to capacitive sensing. A measurement configuration, based on a Wheatstone bridge, as well as an implementation of this measurement scheme to silicon-germanium (SiGe) resonators are also proposed.