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.

Silicon Wafers with Facet‐Dependent Electrical Conductivity Properties

“…These circular wafers have af lat edge.A fter making af ine scratch parallel and perpendicular to the flat edge and applying apressure to break the wafer, sharp edges exposing other crystal facets are obtained. [22,23] Scanning electron microscopy (SEM) images of the Si (100) and (111) wafers after exposing other crystal planes are shown in the Supporting Information, Figure S3. Fort he Si (111) wafer, parallel and perpendicular scribes expose {112} and {110} faces.…”

“…Fort he Si (111) wafer, parallel and perpendicular scribes expose {112} and {110} faces. [22,23] Scanning electron microscopy (SEM) images of the Si (100) and (111) wafers after exposing other crystal planes are shown in the Supporting Information, Figure S3. Clearly sharp faces have been created for subsequent electrical conductivity measurements.…”

Four-Terminal Square Piezoresistive Sensors for MEMS Pressure Sensing

“…This configuration is shown in Figure 4(c). It is shown in detail in [9] that the combination of two adjacent loadings as shown in…”

“…The current is usually supplied at terminals (pads) A and B, and voltage is measured at terminals (pads) C and D. Finally, the resistance ( ) or change in resistance (Δ ) is calculated from CD / AB . It was shown in [9,10] that the normalized resistance change requires two separate measurements with current supplied individually at adjacent sides. Jaeger et al [9] presented numerical and experimental results for four-wire bridge-mode operation (Figure 1(b)) that eliminates two separate resistance measurements required for a traditional square VDP sensor.…”

“…It was shown in [9,10] that the normalized resistance change requires two separate measurements with current supplied individually at adjacent sides. Jaeger et al [9] presented numerical and experimental results for four-wire bridge-mode operation (Figure 1(b)) that eliminates two separate resistance measurements required for a traditional square VDP sensor. It is shown that the output voltage from the four-wire bridge measurements is directly related to the traditional VDP resistance measurements.…”