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Research Papers

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

[+] Author and Article Information
Richard C. Jaeger

Electrical Engineering Department,
Alabama Micro/Nano Science
and Technology Center,
Auburn University,
Auburn, AL 36849
e-mail: rj@jaegerengineering.com

Mohammad Motalab, Safina Hussain, Jeffrey C. Suhling

Mechanical Engineering Department,
Center for Advanced Vehicle and Extreme
Environment Electronics (CAVE3),
Auburn University,
Auburn, AL 36849

We refer to these as van der Pauw sensors since the stress sensor output is directly related to van der Pauw’s original voltage and resistivity results.

Often expressed in terms of infinite series.

Or between any two symmetrically located points on opposite sides of the device.

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received March 2, 2014; final manuscript received August 15, 2014; published online September 19, 2014. Assoc. Editor: Satish Chaparala.

J. Electron. Packag 136(4), 041014 (Sep 19, 2014) (10 pages) Paper No: EP-14-1027; doi: 10.1115/1.4028333 History: Received March 02, 2014; Revised August 15, 2014

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.

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Figures

Grahic Jump Location
Fig. 1

Square VDP devices at 0 deg and 45 deg orientations. (a) (σ'11-σ'22) sensor and (b) σ'12 sensor. Sensor outputs voltage appear between terminals B and D.

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Fig. 2

Principal and primed coordinate systems for (100) silicon

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Fig. 3

Primed coordinate system for (111) silicon

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Fig. 4

Two versions of four-terminal shear stress sensors

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Fig. 5

The diagonal symmetry line across the square

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Fig. 6

Analysis by superposition: (a) diagonal current excitation and (b) + (c) equivalent circuits for superposition

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Fig. 10

Simulated output voltage for the (σ'11-σ'22) stress sensor versus shear stress σ'12 confirming zero response across the diagonal

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Fig. 9

(a) Simulations of the two VDP voltages for 0 deg and 90 deg orientations using the piezoresistive coefficient values in Table 1 for (100) silicon. (b) Simulations of the transverse voltages across the diagonal versus stresses σ'11 and σ'22.

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Fig. 8

Contours of potential distribution for VDP sensor

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Fig. 7

Initial FEA mesh and current excitation I = 100 μA for VDP mode: RVDP = [π/(ln(2)] VDC/IAB

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Fig. 11

Simulated output of the shear stress sensors versus normal stress σ'11

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Fig. 12

Simulated output of the shear sensor versus shear stress when temperature variations are present

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Fig. 13

Transverse output voltage of the normal stress difference sensor versus normal stress (σ'11-σ'22) when temperature variations are present

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Fig. 14

Simulated output error voltage versus σ'11 for rotational misalignment of a shear stress sensor

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Fig. 15

Microphotograph of a VDP test cell containing 0 deg and 45 deg square n-type and p-type sensors on an n-type substrate. Pads are 100 μm x 100 μm.

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Fig. 16

Measured output of a 0 deg n-type sensor on (111) silicon in bridge mode versus uni-axial stress σ'11

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Fig. 17

Measured output of a 0 deg p-type sensor on (111) silicon in bridge mode versus uni-axial stress σ'11

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Fig. 18

45 deg p-type stress sensor on (111) silicon. (a) Measured transverse output voltage across the sensor showing approximately zero response to σ'11. The worst-case output error is −54 μV. (b) Measured output of the same shear stress sensor in VDP mode versus uni-axial stress σ'11.

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Fig. 19

Measured the transverse voltage output of a 45 deg (111) n-type shear stress sensor versus uni-axial stress showing approximately zero response to σ'11. The maximum output error is 35 μV.

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