Application of the van der Pauw structure as a piezoresistive pressure sensor : a numerical study

Abstract

This research characterizes a piezoresistive sensor under variations of both size and orientation with respect to the silicon crystal lattice for its application to MEMS pressure sensing. The sensor to be studied is a four-terminal piezoresistive sensor commonly referred to as a van der Pauw (VDP) structure. It is observed that the sensitivity of the VDP sensor is over three times higher than the conventional filament type Wheatstone bridge resistor. With MEMS devices being used in applications which continually necessitate smaller size, characterizing the effect of size and orientation of a VDP structure on the performance of a MEMS pressure sensor is important. Due to the limitations of anisotropic etching, silicon diaphragms on which the sensors are fabricated must be rectilinear, and most commonly, square. The sensitivity of the VDP stress sensor is affected by misalignment during the etching/diffusion process and by the size of the sensor relative to the size of the underlying pressure diaphragm.

Smaller VDP sensors are able to resolve smaller variations in the stress field, but at diminishing size, manufacturing limitations become important. In this study, we characterize the effect of size and orientation on the sensitivity of the VDP sensor to pressure. In characterizing the effect of relative size and misalignment on the sensitivity of the VDP sensor, a coupled piezoresistive/stress finite element model is developed which simulates the full stress field over the deformed diaphragm in which the VDP is diffused. The change in resistivity of the VDP is then analyzed to predict the sensitivity of the VDP structure. Sensor size, position relative to the diaphragm, and angular misalignment of the VDP were varied to determine a theoretical result for the dependence of VDP output on those parameters. It is determined that the performance of the sensor is strongly dependent only on the longitudinal position of the sensor on the diaphragm, and is relatively tolerant of other errors in the manufacturing process such as transverse position, sensor depth, and orientation angle.