5 Strain Pressure

8/12/2019 5 Strain Pressure

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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

EYoungs modulus of the material

AF

Exx 1


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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

Across sectional area

After differentiating

or

Because

then

Introducing the Poissons number one obtains

R xA

dR

R

dxx

dAA

d

A r 2 dA rdr 2

dR

R

dx

x

dr

r

d

2

d

AxdA

A

xdxA

dRdAARdx

xRdR

2

drr

dxx

drr


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dR

R

d

2

d121RdR

eS

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/RT)

high mechanical durability

Manganinalloy consisting of: 84%Cu + 12%Mn + 4%Ni

Constantan: 60%Cu + 40%Ni

Characteristics of typical alloy strain

gauges

manganin (solid line), Se= 2

constantan (dashed line), Se= 0.8


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Examples of metallic strain gauges

Foil - type

(etched metallic foil

on a backing film)

Rosette - type Thin film


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Piezoresistance in semiconductors

Semiconductor strain gauges have about 50 times higher gauge factorthan metals (typical value of Seis 100).

Drawbacks:

Sedepends on (nonlinearity)

strong temp. dependence

lower dynamic range of .

For a given semiconductor Sedepends on its crystallographic orientation

and doping. In this case the variations of /are important

ddRdR

eS 1121


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Stresses cause change in a band structure of the silicon crystal what

influences the mobility and concentration of current carriers. In effect theresistivity changes but the current density vector j and electric field

vector E are no longer parallel (effect of anisotropytensor description).

)(j)(jE

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- tensor of piezoresistane coefficients

- stress

Piezoresistance in silicon


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Only one stress comp.,longitudinal effectLL

In general the piezoresistive

coeff. depend on crystal

orientation, the type of doping

and change significantly from

one direction to the other.

Piezoresistance in silicon

.compstressorthogonalandparallel, TL

.coefftivepiezoresislarperpendicu

.coefftsivepiezoresisparallel

T

L

TTLL

L T

Diffusive piezoresistor under

parallel and orthogonal stress


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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, belownegative.

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.

t - streching

c- compression


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Wheatstone bridge with four active arms

(increase in sensitivity, temperature offset compensation).

Identical sensors undergo the influence of compressive and

tensile stresses.

thermmech R

R

R

R

R

R

Strain gauges in a bridge connection, cont.


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Changing

doping one can

change sign of

the effect

Compensation of nonlinearity in

semiconductor piezoresistors

Fully compensated bridge based on n-Siand p-Si piezoresistors


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Membrane pressure sensors

Two resistors have their primary axes

parallel to the membrane edge,resulting

in a decrease in resistance with membranebending. The other two resistors

have their axes perpendicular to the edge,

which causes the resistance to increase

with the pressure load.

Distribution of stresses in a

circular membrane under the

influence of applied pressure.


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Pressure sensor with diffused

piezoresistive sense elements

in a Wheatstone bridge

configuration.

Silicon micromachined pressure sensors

National Semiconductor Corp. of Santa Clara, California was the firstcompany 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.


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Technology of micromachined pressure sensors

The fabrication process of a typical

pressure sensor.

Technological steps are characteristic tothe integrated circuit industry, with the

exception of the precise forming

of the thin membrane using

electrochemical etching.


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High temperature pressure sensorsMost of commercially available silicon micromachined pressure sensors are workingin a temperature range40to +125C, which covers the automotive and military

specifications. Above 125C the increased leakage current across thep-njunctionbetween 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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An example of pressure sensor used in vaccum measurements,working as a differential capacitor.

M

pr px

10-4 < p < 103Tr

Cmin= 10-5pF (d~ nm)

Vacuum measurements

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5 Strain Pressure