Overview

Test Case

Four p-type silicon piezoresistors R₁-R₄ of length a and width b are placed on a silicon beam (Figure 400: Piezoresistors on a Beam Problem Sketch). The beam of length l and width w is oriented such that its length is in the <110> direction of silicon crystal. The resistors are connected to form a Wheatstone bridge (Figure 401: Wheatstone Bridge Arrangement of Piezoresistors) with a supply voltage V_s. The beam is subjected to a uniform pressure p in the X-direction. Determine the output voltage V_o of the Wheatstone bridge.

Figure 400: Piezoresistors on a Beam Problem Sketch

Figure 401: Wheatstone Bridge Arrangement of Piezoresistors

Analysis Assumptions and Modeling Notes

The resistors areas are modeled using the piezoresistive option of the coupled-field solid PLANE223. The structural part of the beam is modeled using PLANE183. The resistors are connected into a Wheatstone bridge arrangement by coupling the VOLT degrees of freedom on width sides of the resistors. The supply voltage is applied to the master node of the driving electrode.

The applied pressure results in a uniform stress S_x distribution. Two of the resistors (R₂ and R₃) are parallel to the direction of stress, and change their resistance due to the longitudinal piezoresistive effect. Two other resistors (R₁ and R₄) are perpendicular to the applied stress, and change their resistance due to the transverse piezoresistive effect. A static analysis is performed to determine the output voltage V_o. Results are compared to the analytical solution given by

Results Comparison