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5. Strain and Pressure Sensors
Piezoresistivity
Applied stress gives the change in resistance
? F/A ? ?x/x
?R/R (stress)
(strain) In the case of elastic deformations
the Hookes law obeys. For a sample with the
shape of a rod of length x and cross secion A one
can write E
Youngs modulus of the material
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Metallic cylidrical conductor (a wire) changes
its resistance under the influence of applied
stress The resistance x - length of a
conductor A cross sectional
area After differentiating or Because
then Introducing the Poissons number ? one
obtains
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Using ? one can write
In practice one uses the gauge factor Se
(relative change in resistance for unit
deformation)
material constant
For most metals Se 2 (for platinum about
6) The change in resistance is not exceeding 2.
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• Metallic strain gauges should reveal
• appreciable R
• high Se
• low TCR (TCR ?R/R?T)
• high mechanical durability

• Characteristics of typical alloy strain gauges
• manganin (solid line), Se 2
• constantan (dashed line), Se 0.8

Manganin alloy consisting of 84Cu 12Mn
4Ni Constantan 60Cu 40Ni
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Examples of metallic strain gauges
Foil - type (etched metallic foil on a backing
film)
Thin film
Rosette - type
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Piezoresistance in semiconductors

• Semiconductor strain gauges have about 50 times
  higher gauge factor than metals (typical value of
  Se is 100).
• Drawbacks
• Se depends on ? (nonlinearity)
• strong temp. dependence
• lower dynamic range of ?.
• For a given semiconductor Se depends on its
  crystallographic orientation and doping. In this
  case the variations of ??/? are important

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Piezoresistance in silicon
Stresses cause change in a band structure of the
silicon crystal what influences the mobility and
concentration of current carriers. In effect the
resistivity changes but the current density
vector j and electric field vector E are no
longer parallel (effect of anisotropy tensor
description).
? - tensor of piezoresistane coefficients s -
stress
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Piezoresistance in silicon
Only one stress comp.,
longitudinal effect
Diffusive piezoresistor under parallel and
orthogonal stress
In general the piezoresistive coeff. depend on
crystal orientation, the type of doping and
change significantly from one direction to the
other.
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Examples of semiconductor strain gauges
Semiconductor strain gauges printed on a thick
cantilever for measurements of force P. The
stress above neutral axis is positive, below
negative. The resistors are connected in a
Wheatstone brigde configuration.
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Strain gauges in a bridge connection
Wheatstone bridge with two active arms and
identical strain gauges. et - streching ec -
compression
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Strain gauges in a bridge connection, cont.
Wheatstone bridge with four active arms
(increase in sensitivity, temperature offset
compensation). Identical sensors undergo the
influence of compressive and tensile stresses.
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Compensation of nonlinearity in semiconductor
piezoresistors
Fully compensated bridge based on n-Si and p-Si
piezoresistors
Changing doping one can change sign of the effect
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Membrane pressure sensors
Distribution of stresses in a circular membrane
under the influence of applied pressure.
Two resistors have their primary axes parallel
to the membrane edge,resulting in a decrease in
resistance with membrane bending. The other two
resistors have their axes perpendicular to the
edge, which causes the resistance to
increase with the pressure load.
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Silicon micromachined pressure sensors
National Semiconductor Corp. of Santa Clara,
California was the first company which began the
high-volume production of this kind of pressure
sensor in 1974. Recently this market has grown to
tens of million sensors p.a. The vast majority
use piezoresistive elements to detect stress in a
thin silicon diaphragm in response to a pressure
load.
Pressure sensor with diffused piezoresistive
sense elements in a Wheatstone bridge
configuration.
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Technology of micromachined pressure sensors
The fabrication process of a typical pressure
sensor. Technological steps are characteristic to
the integrated circuit industry, with the
exception of the precise forming of the thin
membrane using electrochemical etching.
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High temperature pressure sensors
Most of commercially available silicon
micromachined pressure sensors are working in a
temperature range 40 to 125ºC, which covers
the automotive and military specifications. Above
125ºC the increased leakage current across the
p-n junction between the diffused piezoresistor
and the substrate significantly degrades
performance. At elevated temperatures the
silicon-on-insulator (SOI) technology can be used.
High-temperature pressure sensor in SOI
technology (GE NovaSensor ).
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Vacuum measurements
An example of pressure sensor used in vaccum
measurements, working as a differential capacitor.
10-4 lt p lt 103 Tr ?Cmin 10-5 pF (?d nm)
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