An Analytical Theory of Piezoresistive Effects in Hall Plates with Large Contacts

Figure 5

Finite element model of a resistive device with three contacts at the lower boundary (= -axis). The plots were obtained by FEM simulations with COMSOL MULTIPHYSICS. They show the potential distribution and the current streamlines. The entire upper half plane is conductive with piezoresistance according to (5) and (6a)–(6c) with and the piezoresistive coefficients for low n-doped silicon (, , ). Pure strain is neglected. The outer contacts are 0.15 m long, the center contact is 0.1 m long, and the spacing between contacts is 0.25 m. The thickness into the drawing plane is 1 m. The left contact is forced to 1 V, the right contact is forced to 0 V, and the center contact is floating (i.e., no current flows in or out). The infinite boundary is modeled with infinite elements. The mesh has 1.4 million elements. At zero mechanical stress the center contact is at 0.5 V and the input resistance is . At the output voltage increases 57 nV and the input resistance decreases −2.443%. At the output voltage decreases −56 nV and the input resistance decreases −2.441%. At the output voltage decreases −2.5 µV and the input resistance decreases −1.218%. All these resistance changes deviate less than 10 ppm from theory (12a)–(12c). The changes in output voltage should be zero according to theory and the small deviations are probably due to insufficiently fine mesh.