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1Electronics and Cybernetics

Denne forelesningen

Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen

Piezoresistivitets tensoren ”Vanlig” målebro

Rotasjon til 110 akser Overgang til ”forenklede” koeffisienter Følsomheten til en ”vanlig” sensor

X-ducer Virkemåte Transformasjon av stresset Følsomheten til en Motorola MAP sensor


Piezoresistive pressure sensors


Modellering av trykkmembran

1mm*1mm*20µm~1018atomer(masser og fjærer)

3 D kontiniumsmekanikk

0)()( 2 uu

),,( zyxu

),( yxw

2 D Plateligning

w r( )3

16 p

1 2

E t3

a2

r2 2

eksakt

varia

sjon

sprin

sipp

stress

FE

M m

odel

lerin

g


Stress (σxx) i trykkmembranen

x


Isotrop resistivitet

Vd

VE d EJ

1


Anisotrop resistivitet

E

J


The resistivity changes with the mechanical stress E - electric field, three components j - current density, three

components 0 – homogeneous resistivity,

unstressed silicon

When mechanical stress is applied, the resistivity changes depending on the stress in different directions and the piezo coefficients

3

2

1

345

426

561

0

3

2

1

0

3

2

1

j

j

j

ddd

ddd

ddd

j

j

j

E

E

E

V1 V2


Silicon: Three independent piezoresistive coefficients

Example of piezoresistive coefficients:

doping: p-type sheet resistivity: 7.8 cm

value of 11= 6.6 10-11 Pa-1

value of 12=-1.1 10-11 Pa-1

value of 44= 138 10-11 Pa-1

Equations 18.3, 18.4, 18.5 in Senturia

xy

zx

yx

z

y

x

d

d

d

d

d

d

44

44

44

111212

121112

121211

6

5

4

3

2

1

00000

00000

00000

000

000

000

3

2

1

345

426

561

0

3

2

1

0

3

2

1

j

j

j

ddd

ddd

ddd

j

j

j

E

E

E


Forenklet beskrivelse

Hvis det er “bestemt” hvilken retning vi vil legge motstandene i, ønsker vi et enklere uttrykke

Transverse and longitudinal coefficients

ttllR

R

The resistor axis is defined according to the direction of

the current through the resistor

lt J


Rotasjon

Stress er opplinjert etter sidekantene som er (110)

Piezokoeffisientene er relatert til (100) akser

Kan rotere piezo koeffisientene


Resistors along <110> direction in (100) wafers

Much used direction for piezoresistors, bulk micromachining

Pre-calculated longitudinal and transverse piezo-coefficients

positive: tensile stress negative: compressible stress positive: increased resistivity with

tensile stress negative: decreased resistivity

with tensile stress

)(2/1

)(2/1

441211

441211

t

l


Båndstruktur og resistivitet

Stor forskjell på n- og p- type silisium


”Doping” av Al


p-type Si

)(2

)(2/1

)(2/1

44

441211

441211

tl

t

l

R

R


Piezoresistor placed normal to diaphragm edge

Apply pressure from above Diaphragm bends down Piezoresistor is stretched longitudinally l is positive, tensile stress Rough argument for mechanical stress in

transversal direction: stress must avoid contraction: t= l

Transverse stress is tensile/positive Change in resistance:

(t is negative) Resistance increases

ltlRR )(/ 11 ttllR

R

p-type piezoresistor along <100> direction in (100) wafer


Piezoresistor placed parallel to diaphragm edge

Apply pressure from above Diaphragm bends down Piezoresistor is stretched transversally t is positive

Rough argument for mechanical stress in longitudinal direction: stress must avoid contraction: l= t

Tensile, positive stress in longitudinal dir. Change in resistance:

(t is negative)

Resistance decreasestltRR )(/ 22

p-type piezoresistor along <100> direction in (100) wafer


Wheatstone bridge circuit

R

RVV

RRR

RRR

RRR

RRR

RR

R

RR

RVV

s

s

0

44

33

22

11

43

3

12

20


Electronics (Chapter 14.1 - 14.4) Doped resistors

Define a p-type circuitin a n-type wafer

n-type wafer must be at positivepotential relative to the p-type circuit

Reverse biased diode no current between circuit and wafer/substrate

+V-

n p

Alternative methods:•SOI•Surface micromachining


Motstandsposisjon og lednigsføring


Forventet følsomhet

PH

L

V

V

s

2

44 3.018.09.02

Pi44

20.9 0.8 1 0.23( ) 0.3

1mm

20m

2

0.2871

V

mV

kPa


X-ducer

[100]=1

• Resistor langs 100 akse

• Har allerede piezo koeffisientene i dette aksesystemet

LR

wR

R

R

R

R

L

w

V

V

wJdEV

LJdEV

1244

1

2

1124422

111

2

1


Men vi må rotere stresset

100


Forventet følsomhet


Re-design


Dependence of piezoresistivity on doping


Pressure Measurement in MedicineExample: Hydrocephalus

abnormal accumulation of brain fluid increased brain pressure occurs in approximately one out of 500

births treated by implantation of a shunt

system


Complex requirements for the measurement system

Small dimensions Effective pressure transmission No wires through the skin No batteries Material acceptable for MRI scans


The sensor

Piezoresistive Surface micro machined Wheatstone bridge

two piezoresistors on diaphragm two on substrate for temperature

reasons Absolute pressure sensor


Sensor design


Sensor design

Si3N4SiO2polySi

(Al)

(polySi)

(not to scale)


Polysilicon

Silicon exists in any of three forms: monocrystalline silicon poly crystalline silicon, also called

polysilicon or poly-Si amorphous

The extent of regular structure varies from amorphous silicon, where the atoms do not even have their nearest neighbors in definite positions, to monocrystalline silicon with atoms organized in a perfect periodic structure.


Piezoresistivity in polysilicon

The piezoresistive coefficients loose sensitivity to crystalline direction

Average over all orientations Gauge factor of 20 – 40, about one fifth of

the gauge factor of monocrystalline silicon Gauge factor up to 70% of monosilicon has

been reported The structure; i.e. the grain size and the

texture (preferred orientation of the crystallites) is decisive for the piezoresistivity

The longitudinal gauge factor is always larger than the transverse one


Functionality & sensitivity

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