electronics and cybernetics 1 denne forelesningen membranbaserte piezoresistiv trykksensor...
TRANSCRIPT
![Page 1: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/1.jpg)
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
![Page 2: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/2.jpg)
2Electronics and Cybernetics
Piezoresistive pressure sensors
![Page 3: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/3.jpg)
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
![Page 4: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/4.jpg)
4Electronics and Cybernetics
Stress (σxx) i trykkmembranen
x
![Page 5: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/5.jpg)
8Electronics and Cybernetics
Isotrop resistivitet
Vd
VE d EJ
1
![Page 6: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/6.jpg)
9Electronics and Cybernetics
Anisotrop resistivitet
E
J
![Page 7: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/7.jpg)
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
![Page 8: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/8.jpg)
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
![Page 9: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/9.jpg)
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
![Page 10: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/10.jpg)
13Electronics and Cybernetics
Rotasjon
Stress er opplinjert etter sidekantene som er (110)
Piezokoeffisientene er relatert til (100) akser
Kan rotere piezo koeffisientene
![Page 11: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/11.jpg)
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
![Page 12: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/12.jpg)
15Electronics and Cybernetics
Båndstruktur og resistivitet
Stor forskjell på n- og p- type silisium
![Page 13: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/13.jpg)
16Electronics and Cybernetics
”Doping” av Al
![Page 14: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/14.jpg)
17Electronics and Cybernetics
p-type Si
)(2
)(2/1
)(2/1
44
441211
441211
tl
t
l
R
R
![Page 15: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/15.jpg)
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
![Page 16: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/16.jpg)
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
![Page 17: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/17.jpg)
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
![Page 18: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/18.jpg)
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
![Page 19: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/19.jpg)
22Electronics and Cybernetics
Motstandsposisjon og lednigsføring
![Page 20: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/20.jpg)
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
![Page 21: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/21.jpg)
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
![Page 22: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/22.jpg)
25Electronics and Cybernetics
Men vi må rotere stresset
100
![Page 23: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/23.jpg)
26Electronics and Cybernetics
Forventet følsomhet
![Page 24: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/24.jpg)
27Electronics and Cybernetics
Re-design
![Page 25: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/25.jpg)
28Electronics and Cybernetics
Dependence of piezoresistivity on doping
![Page 26: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/26.jpg)
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
![Page 27: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/27.jpg)
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
![Page 28: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/28.jpg)
31Electronics and Cybernetics
The sensor
Piezoresistive Surface micro machined Wheatstone bridge
two piezoresistors on diaphragm two on substrate for temperature
reasons Absolute pressure sensor
![Page 29: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/29.jpg)
32Electronics and Cybernetics
Sensor design
![Page 30: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/30.jpg)
33Electronics and Cybernetics
Sensor design
Si3N4SiO2polySi
(Al)
(polySi)
(not to scale)
![Page 31: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/31.jpg)
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.
![Page 32: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/32.jpg)
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
![Page 33: Electronics and Cybernetics 1 Denne forelesningen Membranbaserte piezoresistiv trykksensor (våtetset) Stressfordelingen Piezoresistivitets tensoren ”Vanlig”](https://reader030.vdocuments.net/reader030/viewer/2022032517/56649c815503460f9493845e/html5/thumbnails/33.jpg)
36Electronics and Cybernetics
Functionality & sensitivity