Four-Wire Bridge Measurements of van der Pauw Stress Sensors on (100) and (111) Silicon

Four-wire resistance characterization of van der Pauw stress sensors is discussed. Under the proper orientations and excitations, the output of the four-contact sensors can be shown to depend upon only the in-plane shear stress or the in-plane normal stress difference on (100) silicon. The other stress terms are cancelled out by the symmetry of the structure, and the measurements are inherently temperature compensated. In bridge-mode, each sensor requires only one measurement and produces an output voltage that is directly proportional to the shear stress or in-plane normal stress difference, and the sensitivity is 3.16 times that of the equivalent resistor sensors, just as in the normal van der Pauw mode. Experimental, theoretical, finite-difference and finite-element and simulation results are presented demonstrating the behavior of the sensor. The two sensors can be merged into one eight-contact device, or n- and p-tye sensors can be overlaid in standard IC processes. Similar results apply to sensors on (111) silicon.