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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
2Electronics and Cybernetics
Piezoresistive pressure sensors
3Electronics and Cybernetics
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
4Electronics and Cybernetics
Stress (σxx) i trykkmembranen
x
8Electronics and Cybernetics
Isotrop resistivitet
Vd
VE d EJ
1
9Electronics and Cybernetics
Anisotrop resistivitet
E
J
10Electronics and Cybernetics
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
11Electronics and Cybernetics
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
12Electronics and Cybernetics
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
13Electronics and Cybernetics
Rotasjon
Stress er opplinjert etter sidekantene som er (110)
Piezokoeffisientene er relatert til (100) akser
Kan rotere piezo koeffisientene
14Electronics and Cybernetics
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
15Electronics and Cybernetics
Båndstruktur og resistivitet
Stor forskjell på n- og p- type silisium
16Electronics and Cybernetics
”Doping” av Al
17Electronics and Cybernetics
p-type Si
)(2
)(2/1
)(2/1
44
441211
441211
tl
t
l
R
R
18Electronics and Cybernetics
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
19Electronics and Cybernetics
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
20Electronics and Cybernetics
Wheatstone bridge circuit
R
RVV
RRR
RRR
RRR
RRR
RR
R
RR
RVV
s
s
0
44
33
22
11
43
3
12
20
21Electronics and Cybernetics
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
22Electronics and Cybernetics
Motstandsposisjon og lednigsføring
23Electronics and Cybernetics
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
24Electronics and Cybernetics
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
25Electronics and Cybernetics
Men vi må rotere stresset
100
26Electronics and Cybernetics
Forventet følsomhet
27Electronics and Cybernetics
Re-design
28Electronics and Cybernetics
Dependence of piezoresistivity on doping
29Electronics and Cybernetics
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
30Electronics and Cybernetics
Complex requirements for the measurement system
Small dimensions Effective pressure transmission No wires through the skin No batteries Material acceptable for MRI scans
31Electronics and Cybernetics
The sensor
Piezoresistive Surface micro machined Wheatstone bridge
two piezoresistors on diaphragm two on substrate for temperature
reasons Absolute pressure sensor
32Electronics and Cybernetics
Sensor design
33Electronics and Cybernetics
Sensor design
Si3N4SiO2polySi
(Al)
(polySi)
(not to scale)
34Electronics and Cybernetics
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.
35Electronics and Cybernetics
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
36Electronics and Cybernetics
Functionality & sensitivity