Integrated Piezoresistive Flexure Model in Polysilicon

This paper presents a new model and test device for determining piezoresistive response in long, thin polysilicon beams with axial and bending moment inducing loads. If the piezoresistive coefficients are known, the Integrated Piezoresistive Flexure Model (IPFM) is used to find the new resistance of a beam under stress. The IPFM first discretizes the beam into small volumes represented by resistors. The stress that each of these volumes experiences is calculated, and the stress is used to change the resistance of the representative resistors according to a second-order piezoresistive equation. Once the resistance change in each resistor is calculated, they are combined in parallel and series to find the resistance change of the entire beam. If the piezoresitive coefficients are not initially known, data are first collected from a test device. Piezoresistive coefficients need to be estimated and the IPFM is run for the test device’s different stress states giving resistance predictions. Optimization is done until changing the piezoresistive coefficients provides model predictions that accurately match experimental data. These piezoresistive coefficients can then be used to design and optimize other piezoresistive devices. A sensor is optimized using this method and is found to increase voltage response by an estimated 10 times.