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Micro/Nanosystems Technology Wagner / Meyners 1
Micro/Nanosystems Technology
Prof. Dr. Bernhard Wagner
Dr. Dirk Meyners
Pressure sensors
Micro/Nanosystems Technology Wagner / Meyners 2
Outline
Membrane type pressure sensor
Stress distribution in membrane
Bulk-micromachined piezoresistive pressure sensor
Wheatstone bridge and implementation
Surface-micromachined piezoresistive pressure sensor
Capacitive pressure sensors
Silicon microphones
Micro/Nanosystems Technology Wagner / Meyners 3
Membrane type pressure sensor
1 bar = 105 Pa (N/m2)
= 750 torr (mmHg)
= 14.50 psi (lbs/in2)
= 0.987 atm
Measurement of p2 relative to p1
absolute pressure sensor: p1 = 0 (vacuum)
gauge pressure sensor: p1 = atmospheric pressure (not constant)
differential pressure sensor: p1 = reference pressure
p2
p1
Micro/Nanosystems Technology Wagner / Meyners 4
Bending of thin plates
model
circular plate:
rigid clamping:
uniform pressure loading: p = p2 - p1
R: radius
h: thickness
E: Young’s modulus
: Poisson’s ratio
analytical solution For small deflections: w
Micro/Nanosystems Technology Wagner / Meyners 5
Stress distribution
p
R
r
h
Rr
)1()3(
8
32
2
2
2
pR
r
h
Rt
)1()31(
8
32
2
2
2
Radial stress at plate surface
Tangential stress at plate surface
Max. at clamping r=R ph
Rr 2
2
max,4
3
ph
Rt 2
2
max,8
)1(3
Max. in center r=0
Middelhoek 3.19
r
t
Neutral fiber is stress free
Micro/Nanosystems Technology Wagner / Meyners 6
Stress and strain for rigidly clamped plates
x, x
y = 0
y 0 0
E
E
xy
y
yx
x
at clamping point
xx
xx
xy
E
E
2
2
1
1
0
stresses have same sign!
Senturia, Microsystem design, Ch. 9.5
Round membrane: ph
RRr 2
2
4
3)( )(
4
3)(
2
2
Rph
RR rt
21
Eplate modulus
Micro/Nanosystems Technology Wagner / Meyners 7
Square membranes
Center deflection Max. edge stress
Round membrane
radius R
Square membrane
half width a
ph
Rr 2
2
4
3
ph
ar 2
2
23.1
ph
R
Ew
3
42 )1(
16
3
ph
a
Ew
3
42 )1(242.0
Rigid clamping
Only approximate solutions (e.g. Roark, Formulas for stress and strain)
Micro/Nanosystems Technology Wagner / Meyners 8
Bulk-micromachined piezoresistive pressure sensor
bond pads
p-typesilicon
pyrex glassbacksidehole
etchedcavity
(100) siliconmembrane
p-type diffusedpiezoresistor
metal conductors
(111) siliconplane
n-typeepitaxiallayer
Piezoresistivity is dominating
signal conversion principle
Silicon membrane
Usually square shape
Edge length: 1-2mm
2-20 µm thick
Wet anisotropic Si etch + etch stop
Piezoresistors:
Single crystalline Si with pn-isolation
Micro/Nanosystems Technology Wagner / Meyners 9
Process flow for piezoresistive pressure sensor
Beeby Fig. 4.9
Etch stop at pn-junction
Up to 3 implantations:
1) piezoresistors: p (B)
2) bridge interconnection: p+ (B)
3) metal contact: n+ (Ph)
3
1 2
Micro/Nanosystems Technology Wagner / Meyners 10
Small size pressure sensors
Standard wet etched sensor
(wet etching from backside)
outward inclined sidewalls
Large area consumption
Dry etched sensor
(deep reactive ion etching, DRIE)
Vertical sidewalls
Etch stop on SiO2 of SOI wafer
Reduced chip size, higher cost in etching step
Waferbonded sensor
inward inclined sidewalls
SOI wafer is fusion bonded on wafer with cavity
Substrate of SOI wafer is removed
Micro/Nanosystems Technology Wagner / Meyners 11
Specific pressure sensors
High temperature sensor
pn-junction isolation only useful up to + 125°C, due to thermal carrier generation
Dielectric isolation between resistor and Si membrane needed
Resistor material: SOI-Si, poly-Si, SiC, …
High pressure sensor (p > 100 bar)
Fusion bonded wafers (Si-Si bonding)
with enclosed shallow cavity
Micro/Nanosystems Technology Wagner / Meyners 12
Wheatstone bridge
inout VRRRR
RRRRV
))(( 4321
4231
Symmetric bridge:
place resistors in such a way that
R1= R3 and R2 = R4
ininout VRR
RRV
RR
RRV
21
21
2
21
2
2
2
1
)(
In ideal case R1 and R2 should have opposite pressure sensitivity S
R1= R0(1 + S∙p) R2 = R0(1 - S∙p)
pSVV inout /Signal is directly proportional to pressure
Independent of resistor absolute value
Temperature dependence of resistors (TCR) cancels out
Micro/Nanosystems Technology Wagner / Meyners 13
Resistors with opposite pressure dependence
Two possibilities:
Choose positions with opposite stress: tensile and
compressive
Combine longitudinal and transverse piezoresistors with same
stress
Gauge factor of p-doped resistors is nearly opposite
transtranslonglong
long -trans
Micro/Nanosystems Technology Wagner / Meyners 14
Wheatstone bridge implementation
Resistor arrangements for square membrane
R1 and R3 are longitudinal piezoresistors
R2 and R4 are transverse piezoresistors
2
1
4
3
R1
R2 R4
R3
Interconnection lines to piezoresistors on membrane:
high doped Si or metal (might cause stress)
Micro/Nanosystems Technology Wagner / Meyners 15
Sensor characterisation
sensitivity S in mV/V/bar
offset voltage Voffset
full scale output: Vf.s. nominal pressure: pf.s.
TCO: temperature coefficient of offset
TCS: temperature coefficient of sensitivity
Vout
p
T1 T2
Ideal: Vout = Vin Sp
Real: Vout = Vin aoffset (1+ T•TCO) + S(1 + T•TCS)p + nonlinear terms
Vout
p Voffset
T = Tref = 20°C
S0
S1
Vf.s.
Pf.s.
Micro/Nanosystems Technology Wagner / Meyners 16
Sensor calibration
Calibration: compensation of sensor temperature drifts and nonlinearity
Measurement of Vout at least at two pressures and two temperatures
=> S, Voffset, TCO, TCS
Non-linear characteristics requires
more calibration measurements => higher cost
Calibration has to be performed
after packaging on chip-level => high cost
temperature drifts are often caused by packaging
Analog calibration: laser trimming of external resistor network
Digital signal conditioning: integration of sensor with ASIC
calibration + amplification + digital conversion
monolithic or hybrid integration
Micro/Nanosystems Technology Wagner / Meyners 17
Non-linear (large) deflection of thin plates
Assumption: no intrinsic stress
Linear term: due to plate bending (bending stress)
neutral fiber is stress free
Cubic term: due to plate stretching (membrane stress, also in neutral fiber)
For high pressures (deflections): w ~ p1/3
....
5
13
3
16
1
34
2 h
w
h
w
R
h
v
Ep
Micro/Nanosystems Technology Wagner / Meyners 18
Non-linear deflection: example
Si membrane: R= 250 µm, h= 0.5µm, E= 170 GPa, =0.3
linear theory: w = 0.031 µm/Pa
20% deviation at
center deflection w=h
linear theory is only good
approximation for w < 0.2h Non-linear theory
Micro/Nanosystems Technology Wagner / Meyners 19
Low-pressure sensors
p < 30 mbar
For low pressure sensors membranes have to be very thin
non-linear performance
Solution:
Membrane with stiff center part
bossed membrane or ring membrane
limits the maximum deflection
improves linearity
reduces sensitivity
p
flat membrane
bossed membrane
V
Micro/Nanosystems Technology Wagner / Meyners 20
Bossed membranes
S-shaped membrane deflection:
Radial stress at outer membrane radius R is equal
and opposite to stress at inner radius R0
Circular ring membrane
ph
RRRR rr 2
2
0
2
04
3)()(
Placement of resistors
for Wheatstone bridge
R0 R
1 2 3 4
R1 and R2 have opposite stress
Micro/Nanosystems Technology Wagner / Meyners 21
Rectangular bossed membranes
Anisotropically etched membrane
with center boss
4
3
Etched silicon boss structure
Edge compensation structures needed
Resistor placement for membrane with
rectangular boss
1
2
Micro/Nanosystems Technology Wagner / Meyners 22
Monolithically integrated pressure sensor
Bosch SMD085
Absolute piezoresistive pressor sensor
On-chip signal conditioning IC
Temperature and offset compensation
Pressure range: 0.6 …1.15 bar
piezoresistors
Micro/Nanosystems Technology Wagner / Meyners 23
Surface micromachined piezoresistive sensor
Poly-Si piezoresistors in poly-Si membrane (dielectric isolation)
Poly-Si + SiO2 sacrificial layer
LPCVD SiO2 etch hole sealing
PECVD-Si-Oxynitride passivation
Lisec, Fraunhofer-ISIT 1996
Micro/Nanosystems Technology Wagner / Meyners 24
Surface micromachined piezoresistive sensor
Packaged catheter-tip
blood pressure sensor
Chip size: 0.4 x 2.3 mm
Pressure range 0… 1bar
Supply voltage 2.0 V
Full scale signal FS 15 mV
Sensitivity 7.5 mV/V/bar
Offset 70 mV
Non-linearity
Micro/Nanosystems Technology Wagner / Meyners 25
Piezoresistive pressure sensors
Advantages:
high sensitivity
easy to implement in technology
signal conditioning can be distant from sensor element
Disadvantages:
high power consumption
high temperature cross-sensitivity
high packaging stress sensitivity
Micro/Nanosystems Technology Wagner / Meyners 26
Capacitive pressure sensors
Parallel plate capacitors
Surface and bulk
micromachined devices
Advantages:
low temperature drift
low power
Disadvantages:
nonlinear output
high stray capacitances
signal conditioning has to be close to sensor cell
yxpyxwd
dxdypC
,
0),,(
)(
d: gap at p=0
w: deflection
Micro/Nanosystems Technology Wagner / Meyners 27
Surface micromachined capacitive pressure sensor
Fraunhofer IMS
membrane diameter: 25 … 120 µm
depending on pressure: 350 bar …1 bar
Micro/Nanosystems Technology Wagner / Meyners 28
Touch mode capacitive pressure sensor
Linear increase of contact area linear sensor characteristics
Micro/Nanosystems Technology Wagner / Meyners 29
Integrated capacitive pressure sensor
pressure sensor cells
+ reference capacitor cells
On-chip CMOS IC for linearization, amplification,
temperature and offset compensation,
storage of calibration data in EEPROM
Fraunhofer IMS
Chip size: 2.9mm x 3.1 mm
Micro/Nanosystems Technology Wagner / Meyners 30
Silicon microphones
Pressure range (dynamic range):
Sound pressure level (SPL)
Definition:
0 dB SPL p = 20 µPa lower threshold of human ear
94 dB SPL p = 1 Pa
120 dB SPL p = 20 Pa
Frequency range (bandwidth):
20 Hz – 20 kHz frequency range of human ear
Pa
PapdBSPL
20log20)(
Microphones specification:
extreme low-pressure sensor: p < 10 Pa
high dynamic range: SPL = 35 dB ...110 dB
high bandwidth: 20 kHz
Micro/Nanosystems Technology Wagner / Meyners 31
Capacitive (condensor) microphone
p (sound = acoustical pressure fluctuation)
Capacitor is formed between
diaphragm: thin flexible membrane (Si, SiN, polymer)
back-plate: rigid counter electrode
Capacitive microphones are in volume production
Piezoelectric microphones have been realized on research level
Micro/Nanosystems Technology Wagner / Meyners 32
Microphone design
considerations
Measurement of dynamic pressure difference between membrane frontside
and backside (backchamber pressure)
Backplate has to have large openings (~ 30% of area)
to allow air flow from gap to backchamber
backplate can also be on top of membrane
Backside of membrane has to be encapsulated
from sound pressure to avoid acoustic short cut => introduce back chamber
Backchamber volume should have a certain value: V 0.5 mm3
otherwise it reduces the membrane deflection due to air cushion
Backchamber or membrane has to have a small hole to allow equalization
between ambient pressure and backchamber pressure
Micro/Nanosystems Technology Wagner / Meyners 33
Membrane design
High sensitivity thin membrane or beam suspended plate
openings in membrane must be very narrow
Resonant frequency > 20 kHz introduce tensile stress
no boss structure
Thin membrane under tensile stress : Deflection w0 and resonant frequency is strongly influenced by stress
(already for stresses in the order of 1-10 MPa)
3
04304
3
2021w
R
Ehcw
R
Ehcw
R
hcp
Round membrane:
stress term small deflection
bending term
large deflection
stretching term )1(5
13
)1(3
16
4
23
22
1
c
c
c
Micro/Nanosystems Technology Wagner / Meyners 34
Realisation of silicon microphone (example)
A. Torkkeli, Sensors & Actuators, 85(2000)116
Backplate (thick poly-Si)
(thin poly-Si)
Size: 1 mm x 1mm
Micro/Nanosystems Technology Wagner / Meyners 35
Microphone fabrication process
Micro/Nanosystems Technology Wagner / Meyners 36
Commercial microphone
Knowles Acoustics
chip size: 1.1 mm2
Other manufacturers: SonionMEMS (Epcos), Infineon, Akustica (Bosch),
Analog Device, ST Microelectronics
Micro/Nanosystems Technology Wagner / Meyners 37
Microphone applications
Mobile phones, headsets
notebooks, cameras
Automotive hands-free sets
Hearing Instruments
Directivity:
direction dependence of sensitivity
usually silicon microphones are omnidirectional
i.e. have no directivity
Microphone arrays: 2 microphones
Adaptive change of directivity
Recognition of sound direction
Tracking of human speaker
Noise suppression
90°
60°
30°
0°
270°
180°
0 dB
-10
-20
-30
Silicon microphone array sensitivity
90°
60°
30°
0°
270°
180°
0 dB
-10
-20
-30
Silicon microphone array sensitivity
90°
60°
30°
0°
270°
180°
0 dB
-10
-20
-30
Silicon microphone array sensitivity
90°
60°
30°
0°
270°
180°
0 dB
-10
-20
-30
Silicon microphone array sensitivity
90°
60°
30°
0°
270°
180°
0 dB
-10
-20
-30
Silicon microphone array sensitivity
90°
60°
30°
0°
270°
180°
0 dB
-10
-20
-30
Silicon microphone array sensitivity
Sonion MEMS
Micro/Nanosystems Technology Wagner / Meyners 38
Summary
Bulk and surface micromachined pressure sensors
Piezoresistive sensors are dominating
Placement of piezoresistors in Wheatstone bridge
to minimize offset and compensate TCR
Sensor calibration needed for TCO and TCS compensation
Nonlinear characteristics already for small deflections
Capacitive sensors are advantageous for low-power applications
Microphone is ultra-low differential pressure sensor
capacitive microphones dominating
Monolithic integration of pressure sensor and IC is feasible
Micro/Nanosystems Technology Wagner / Meyners 39
Literature
S.D. Senturia Microsystem Design, Ch. 9.5
H.-J. Timme CMOS-based pressure sensors
in O. Brand, G.K. Fedder (eds.): CMOS-MEMS
S. Beeby et al. MEMS mechanical sensors, Ch. 6