Download Piezoresistive pressure sensors

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
Electronics and Cybernetics
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Piezoresistive pressure sensors
Electronics and Cybernetics
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Modellering av trykkmembran

u ( x, y , z )


(   )(  u )   2u  0
3 D kontiniumsmekanikk
1mm*1mm*20µm
~1018atomer
(masser og fjærer)
w( x, y)
2 D Plateligning
w ( r)

3
16
p
1
E t
3
2
a2  r22
stress
Electronics and Cybernetics
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Stress (σxx) i trykkmembranen
x
Electronics and Cybernetics
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Isotrop resistivitet
d
 1 
J E

E
V
d
V
Electronics and Cybernetics
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Anisotrop resistivitet

J

E
Electronics and Cybernetics
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The resistivity changes with the
mechanical stress
 E - electric field, three components
 j - current density, three
components
 0 – homogeneous resistivity,
unstressed silicon
V1
V2
 When mechanical stress is
applied, the resistivity changes
depending on the stress in different
directions and the piezo
 E1 
coefficients
d1 d 6 d5   j1 
 j1 
 E     j    d d d   j 
0 2
0 6
2
4  2 
 2
d5 d 4 d 3   j3 
 E3 
 j3 
Electronics and Cybernetics
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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
d1 d 6 d5   j1 
 E1 
 j1 
 E     j    d d d   j 
0 2
0 6
2
4  2 
 2
d5 d 4 d 3   j3 
 E3 
 j3 
d1  11 12 12 0 0 0
 d  
11 12 0 0 0
 2   12
d 3  12 12 11 0 0 0
 
0 0  44 0 0
 d 4  0
 d 5  0
0 0 0  44 0
  
d 6  0
0 0 0 0  44
Electronics and Cybernetics
  x 
  
 y 
  z 
 
  yx 
 
  zx 
  xy 
11
Forenklet beskrivelse
 Hvis det er “bestemt” hvilken
retning vi vil legge motstandene i,
ønsker vi et enklere uttrykke
J
t
l
 Transverse and longitudinal
coefficients
R
  l l   t t
R
The resistor axis is defined
according to the direction of
the current through the resistor
Electronics and Cybernetics
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Rotasjon
 Stress er opplinjert etter
sidekantene som er (110)
 Piezokoeffisientene er relatert til
(100) akser
 Kan rotere piezo koeffisientene
Electronics and Cybernetics
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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
 l  1/ 2( 11   12   44 )
 t  1/ 2( 11   12   44 )
Electronics and Cybernetics
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Båndstruktur og resistivitet
Stor forskjell på n- og p- type silisium
Electronics and Cybernetics
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”Doping” av Al
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p-type Si
 l  1 / 2( 11   12   44 )
 t  1 / 2( 11   12   44 )
R  44

( l   t )
R
2
Electronics and Cybernetics
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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:
R
  l l   t t
R
R1 / R1  ( l  t ) l
 (t is negative)
 Resistance increases
p-type piezoresistor along
<100> direction in (100) wafer
Electronics and Cybernetics
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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:
R2 / R2  ( t  l ) t
p-type piezoresistor along
<100> direction in (100) wafer
 (t is negative)
 Resistance decreases
Electronics and Cybernetics
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Wheatstone bridge circuit
 R2
R3 

V0  Vs 

 R2  R1 R3  R4 
R1  R1  R
R2  R2  R
R3  R3  R
R4  R4  R
 R 
V0  Vs  
 R
Electronics and Cybernetics
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Electronics (Chapter 14.1 - 14.4)
Doped resistors
Define a p-type circuit
in a n-type wafer
n-type wafer must be at positive
potential relative to the p-type circuit
n
p
+V-
Reverse biased diode  no current
between circuit and wafer/substrate
Alternative methods:
•SOI
•Surface micromachining
Electronics and Cybernetics
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Motstandsposisjon og lednigsføring
Electronics and Cybernetics
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Forventet følsomhet
V  44
L

0.9  0.8  1    0.3    P
Vs
2
H 
2
Pi44
2
1mm 
1 mV
 0.9 0.8 ( 1  0.23)  0.3 
  0.287
2
V kPa
 20m 
Electronics and Cybernetics
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X-ducer
• Resistor langs 100 akse
• Har allerede piezo
koeffisientene i dette
aksesystemet
[100]=1
wR
V1   E1d1   J1LR
V2   E2 d 2   44 12 J1wR
LR
Electronics and Cybernetics
V2
w
  44 12 R
V1
LR
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Men vi må rotere stresset
100
Electronics and Cybernetics
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Forventet følsomhet
Electronics and Cybernetics
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Re-design
Electronics and Cybernetics
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Dependence of piezoresistivity on
doping
Electronics and Cybernetics
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Pressure Measurement in Medicine
Example: Hydrocephalus
 abnormal accumulation of brain fluid
 increased brain pressure
 occurs in approximately one out of 500
births
 treated by implantation of a shunt
system
Electronics and Cybernetics
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Complex requirements for the measurement
system





Small dimensions
Effective pressure transmission
No wires through the skin
No batteries
Material acceptable for MRI scans
Electronics and Cybernetics
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The sensor
 Piezoresistive
 Surface micro machined
 Wheatstone bridge
 two piezoresistors on diaphragm
 two on substrate for temperature
reasons
 Absolute pressure sensor
Electronics and Cybernetics
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Sensor design
Electronics and Cybernetics
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Sensor design
(polySi)
(Al)
polySi
SiO2
Si3N4
(not to scale)
Electronics and Cybernetics
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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.
Electronics and Cybernetics
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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
Electronics and Cybernetics
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Functionality & sensitivity
Electronics and Cybernetics
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