Four-Wire Bridge Measurements of Silicon van der Pauw Stress Sensors

Abstract

Under the proper orientations and excitations, the transverse output of rotationally symmetric four-contact van der Pauw (VDP) stress sensors depends upon only the in-plane shear stress or the difference of the in-plane normal stresses on (100) silicon. In bridge-mode, each sensor requires only one four-wire measurement and produces an output voltage with a sensitivity that is 3.16 times that of the equivalent resistor rosettes or bridges, just as in the normal VDP sensor mode that requires two separate measurements. Both numerical and experimental results are presented to validate the conjectured behavior of the sensor. Similar results apply to sensors on (111) silicon. The output voltage results provide a simple mathematical expression for the offset voltage in Hall effect devices or the response of pseudo Hall-effect sensors. Bridge operation facilitates use of the VDP structure in embedded stress sensors in integrated circuits.