piezoresistive pressure sensors...piezoresistive measure mechanical stress in doped resistor-area...
TRANSCRIPT
Electronics and Cybernetics 1
Piezoresistive pressure sensors
Electronics and Cybernetics 2
Two sensing principles
Piezoresistive
measure mechanical stress in doped resistor-area
diaphragm pressure sensor
bending beam due to
volume forces (e.g. acceleration)
end force (e.g. protein attached)
capacitive
measure deflection (distance to other capacitor plate)
diaphragm pressure sensor
bending beam due to
volume forces (e.g. acceleration)
end force (e.g. protein attached)
Electronics and Cybernetics 3
Piezoresistive sensing applications
Veieceller AkselerometerTrykksensorer
Electronics and Cybernetics 4
Relation between stress and strain in a coordinate system with axes equivalent to the axes of the unit cell
xy
zx
yz
z
y
x
xy
zx
yx
z
y
x
CC
C
CCC
CCC
CCC
44
44
44
111212
121112
121211
000000000000000
000
000
000
F
x = E x 1D hooke’s law
Electronics and Cybernetics 5
Small deflections Beam equation, plate equation
Beam equation:
Plate equation:
Find displacement and stress
qdx
wdEI 4
4
F
p
),()2( 4
4
22
4
4
4
yxqyw
yxw
xwD
Electronics and Cybernetics 6
General: Finite Element Analysis
Solve Navier’s equation (partial differential equation)
Divide domain into elements
Approximation of function (solution to partial differential equation) over domain
Simple function over each element (linear, parabolic)
Connect elements at nodes
0)()( 2 uu
Electronics and Cybernetics 7
Example: beam with end load
Electronics and Cybernetics 8
Resistor change in metal strain gauges
Mainly due to change of resistor FORM (geometric effect)
aa
L
R0 =
L/a2
F
a+a
L+L
R=R0 +R0 L/L+3R0 a/a
a/a =- L/L
=0.3
R/R
2 L/L R/R
2
Electronics and Cybernetics 9
For silicon: large RESISTIVITY change with stress (not mainly a geometric resistor-change factor)
+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ - + -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ - + -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ - + -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ - + -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -
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+ -
+ -
+ -
+ -
+ -
+ -
+ -
+ -
+ -
+ -
+ -
+ -
+ -
+ -
+ -
+ -
+ -
+ -
+ -
+ -
R/R
2
Metal:
+ +- -
R/R
90
Silicon:
Electronics and Cybernetics 10
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
Electronics and Cybernetics 11
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
jjj
ddddddddd
jjj
EEE
V1 V2
Electronics and Cybernetics 12
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
dddddd
44
44
44
111212
121112
121211
6
5
4
3
2
1
000000000000000
000
000
000
3
2
1
345
426
561
0
3
2
1
0
3
2
1
jjj
ddddddddd
jjj
EEE
Electronics and Cybernetics 13
Dependence of piezoresistivity on doping
Electronics and Cybernetics 14
Long, narrow resistors
Pre-calculated “piezocoefficients” that enables the designer to calculate the resistivity change for a long, narrow resistor
Often given for a resistor that is placed in the <110> direction
Transverse and longitudinal coefficients
ttllRR
Electronics and Cybernetics 15
Resistors in <110> direction
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
p-type silicon: 44 dominates
)(2
)(2/1
)(2/1
44
441211
441211
tl
t
l
RR
Electronics and Cybernetics 16
Beam accelerometer
Long resistors in <110> direction
Piezoresistance coefficients
Electronics and Cybernetics 17
Cantilever with piezoresistors
length 200 m
width 20 m
thickness 5 m
point load at free end
p-type piezoresistor
length 20 m
width 2 m
depth 0.2 m
R/R = l l =0.02
Electronics and Cybernetics 18
Placement of piezoresistors on diaphragm
Over/under konfigurasjoner ikke praktisk i silisium.
Men vi kan snu retningenpå motstandene
Electronics and Cybernetics 19
Stress level at point in structure: Mises yield criterion
213
232
2212/1 mieses
Electronics and Cybernetics 20
x , normal stress on x=const. planes
Electronics and Cybernetics 21
y , normal stress on y=const. planes
Electronics and Cybernetics 22
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
Electronics and Cybernetics 23
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 decreases
tltRR )(/ 22
Electronics and Cybernetics 24
Membrane pressure sensor
Electronics and Cybernetics 25
Wheatstone bridge circuit
<100> direction
RRVV
RRRRRRRRRRRR
RRR
RRRVV
s
s
0
44
33
22
11
43
3
12
20
3.668.71
t
l
stress lecompressib negative, stress tensilepositive,
Electronics and Cybernetics 26
Averaging over stress and doping variations
Senturia 18.2.5
dzz
zLWRRR
jz
lloe0 ,
00 )()(
1
3
2
1
345
426
561
0
3
2
1
0
3
2
1
jjj
ddddddddd
jjj
EEE
Electronics and Cybernetics 27
Motorola MAP sensor
Electronics and Cybernetics 28
Potential across piezoresistor
Electric field in transverse direction
3
2
1
345
426
561
0
3
2
1
0
3
2
1
jjj
ddddddddd
jjj
EEE
Electronics and Cybernetics 29
Coventor tutorials-choose one
In files mems_analy.pdf and mems_supp.pdf (2004 version)
In files MEMS Design and Analysis Tutorials vol1 +2 (2005 version)
Mirror design (electrostatic forces)
Beam simulation analysis (pull-in)
Modal and harmonic analysis (resonant frequencies, modal shapes)
Temperature analysis (temperature distribution, different coefficients)
MemHenry (magnetic sensor)
MemPackage (thermal and mechanical effects)
MemPZR (piezoresistors)
MemETherm (Joule heating, thermal expansion)
AutoSpring (Extract spring constants)
MemDamping (Squeeze film, slide damping)
MemTrans (Transient analysis)