Transcript Prezentacja programu PowerPoint

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 Hooke’s law obeys.
For a sample with the shape of a rod of length x and cross
secion A one can write
x  1 F
x E A
E – Young’s modulus of the material
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Metallic cylidrical conductor (a wire) changes its resistance under the
influence of applied stress
R  x
A
The resistance
After differentiating
or
Because
then
x - length of a conductor
A – cross sectional area
dR   R dx   R dA   R d   dx   x dA  x d
A
A
x
A

A2
dR dx dA d
  
R x A 
A  r 2
dA  2rdr
dR dx 2dr d
 

x
r

R
dr
Introducing the Poisson’s number  one obtains    r     dr
r
dx
x
Using  one can write
dR
   2  d

R
In practice one uses the gauge factor Se (relative change
in resistance for unit deformation):
dR
1
Se  R  1 2  d


material constant
For most metals Se ~ 2 (for platinum about 6)
The change in resistance is not exceeding 2%.
Metallic strain gauges should reveal:
• appreciable R
• high Se
• low TCR (TCR = ΔR/RΔT)
• high mechanical durability
Characteristics of typical alloy strain
gauges
manganin (solid line), Se = 2
constantan (dashed line), Se = 0.8
Manganin – alloy consisting of: 84%Cu + 12%Mn + 4%Ni
Constantan: 60%Cu + 40%Ni
Examples of metallic strain gauges
Foil - type
(etched metallic foil
on a backing film)
Rosette - type
Thin film
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
dR
1
1
Se  R  1 2  d  d

 
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).
 


E  j ( 1 
)  j  ( 1   )

П - tensor of piezoresistane coefficients
σ - stress
Piezoresistance in silicon

  L  L Only one stress comp.,

longitudinal effect

  L L  T T

L ,T  parallel and orthogonal stress comp.
 L  parallel piezoresis tsive coeff .
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.
T  perpendicu lar piezoresis tive coeff .
L
T
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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.
εt - streching
εc - compression
Strain gauges in a bridge connection, cont.
R  R 
 R 

 

R  R mech  R therm
Wheatstone bridge with four active arms
(increase in sensitivity, temperature offset compensation).
Identical sensors undergo the influence of compressive and
tensile stresses.
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 < p < 103 Tr
ΔCmin = 10-5 pF (Δd~ nm)
M
pr
px
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