micro/nanosystems technology · bulk-micromachined piezoresistive pressure sensor ds pe on s de e d...

Micro/Nanosystems Technology Wagner / Meyners 1

Micro/Nanosystems Technology

Prof. Dr. Bernhard Wagner

Dr. Dirk Meyners

Pressure sensors


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


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


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


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


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


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)


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


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


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


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


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


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


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)


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.


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


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


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


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


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


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


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


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


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


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


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


Surface micromachined capacitive pressure sensor

Fraunhofer IMS

membrane diameter: 25 … 120 µm

depending on pressure: 350 bar …1 bar


Touch mode capacitive pressure sensor

Linear increase of contact area linear sensor characteristics


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


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


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


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


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


Realisation of silicon microphone (example)

A. Torkkeli, Sensors & Actuators, 85(2000)116

Backplate (thick poly-Si)

(thin poly-Si)

Size: 1 mm x 1mm


Microphone fabrication process


Commercial microphone

Knowles Acoustics

chip size: 1.1 mm2

Other manufacturers: SonionMEMS (Epcos), Infineon, Akustica (Bosch),

Analog Device, ST Microelectronics


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


90°

60°

30°

0°

270°

180°

0 dB

-10

-20

-30


90°

60°

30°

0°

270°

180°

0 dB

-10

-20

-30


90°

60°

30°

0°

270°

180°

0 dB

-10

-20

-30


90°

60°

30°

0°

270°

180°

0 dB

-10

-20

-30


Sonion MEMS


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


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

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