The van der Pauw stress sensor

Piezoresistive sensors fabricated on (100) and (111) silicon surfaces are capable of measuring from four to all six components of the stress state at a point on the surface of an integrated circuit die. Such resistor-based sensors have been successfully designed and fabricated on these wafer planes and have been used successfully for measurement of die stresses in electronic packages by many research teams. In this paper, classical van der Pauw (VDP) structures, traditionally used for sheet resistance measurement, are shown to provide more than three times the sensitivity of standard resistor sensors. A single four-terminal VDP device replaces two resistor rosette elements and inherently utilizes the high-accuracy four-wire resistance measurement method. Theoretical expressions are developed for the change in resistance of the VDP device as a function of the individual stress components resolved in wafer coordinate systems on both the (100) and (111) silicon surfaces, and it is predicted theoretically that VDP devices will exhibit more than three times higher sensitivity to stress than standard resistor sensors. Design, fabrication, and experimental characterization of VDP and resistor test structures are presented for both silicon surfaces, and numerical simulation is used to help resolve discrepancies between theory and experiment. Sources of experimental error are identified, and the 3.16 times sensitivity enhancement of the VDP device is confirmed.