A Model for Predicting the Piezoresistive Effect in Microflexures Experiencing Bending and Tension Loads

Abstract

This paper proposes a model for predicting the piezoresistive effect in microflexures experiencing bending stresses. Linear models have long existed for describing piezoresistivity for members in pure tension and compression. However, extensions of linear models to more complex loading conditions do not match with experimental results. A second-order model to predict piezoresistive effects in tension, compression, and more complex loading conditions is proposed. A reduced form of the general second-order model is presented for thin flexures in bending. A three-step approach is used to determine the piezoresistive coefficients for this reduced-form model. The approach is demonstrated for two sets of n-type polysilicon. The predictive ability of the model is investigated by comparing the results to the experimental results using the new piezoresistive model and coefficients. One of the ways to implement the model is with multiphysics finite element analysis (FEA). The piezoresistive FEA for flexures algorithm is a FEA implementation of the unidirectional form of the model for flexures. The results presented in this paper are for the simplified cases of long thin flexures experiencing bending and axial loads. This new model could contribute to optimized sensors and feedback control of microdevices, nanopositioning, and self-sensing microdevices.

Piezoresistive Transduction in a Double-Ended Tuning Fork SOI MEMS Resonator for Enhanced Linear Electrical Performance

“…12 shows the resulting linear plot of G m divided by Q against I b , in good agreement with analytic model as captured in (14). Furthermore, the slope of the linear best fit line is defined by (14) and thus we can compare the measured slope against the analytic model prediction. Among the various parameters in (14), the exact values of the capacitive transduction factor (η) and longitudinal piezoresistive coefficient (π l ) are the most uncertain.…”

“…Fig. 12 shows the resulting linear plot of G m divided by Q against I b , in good agreement with analytic model as captured in (14). Furthermore, the slope of the linear best fit line is defined by (14) and thus we can compare the measured slope against the analytic model prediction.…”

“…Furthermore, the slope of the linear best fit line is defined by (14) and thus we can compare the measured slope against the analytic model prediction. Among the various parameters in (14), the exact values of the capacitive transduction factor (η) and longitudinal piezoresistive coefficient (π l ) are the most uncertain. In the case of η, its value is largely affected by the capacitor gap that is subjected to fabrication tolerances.…”

“…It has been shown that it is possible to use the entire body of a vibrating beam MEMS resonator as a strain gauge, whereby the electromechanical conversion is provided by the periodic elongation of the beam along its longitudinal axis [14]. The origin of the piezoresistive conversion can be illustrated by considering the vibration mode shape of the beam, as shown in Fig.…”

Tilted Beam Piezoresistive Displacement Sensor: Design, Modeling, and Characterization

“…In [21] the piezoresistive property of a uniformly doped poly-silicon beam is used for displacement sensing in a MEMS device with thermal actuators. The sensor shows a nonlinear response most likely due to the second-order piezoresistive effect in the bending load, nonlinear displacement dependency of mechanical stress in the sensing beam, and the thermal coupling from actuator to sensor [21], [22]. In [23] and [24], the bulk piezoresistivity of T-shaped flexures are used for vibration detection of the resonators fabricated in the standard SOI-MEMS processes over extremely small displacement ranges.…”