Capacitive sensors and their readout electronics

Aarne Oja

VTT Information TechnologyMicrosensing

aarne.oja@vtt.fi

Contents

• What it’s all about: micromachined capacitive accelometer as an example• Motivation for capacitive MEMS sensors (goodies)• Capacitive readout schemes

• AC readout (displacement measurement)• Direct readout (velocity measurement)• Readout using a tuned circuit• Capacitive sensors based on loss factor measurement• Resonating capacitive sensors

• Basic sensor terminology• Brownian noise of capacitive sensors• Electrostatic actuation (the concept of transducer)

• CV curve of a capacitive transducer• Pull-in voltage

• Measurement techniques related to capacitive sensors• Bridge measurement• Nonlinearity of the capacitive sensor• Force feedback• Guarding against stray capacitances

Motivation for capacitive sensors

• Low power consumption• High resolution• Small temperature coefficient (e.g., in capacitive MEMS sensors)• Possibility for high-volume manufacturing (e.g., by using MEMS

technology)• Potential for low cost• Potential for monolithic integration with readout electronics• Possibility to reuse of IP blocks (i.e., designs) both in IC and MEMS parts• In capacitive MEMS sensors, the dynamic range can be tailored in a wide

range by scaling the dimensions of the MEMS structure

Example: Capacitive pressure sensor

2p

1p

kxAppF =−= )( 12

( )

( ) 4

3

2max

3

42

1316

1613

RdEtp

txEtpRx

ν

ν

−=∆

<

∆−=

“Convenient” measuring range (dynamic range) for a Si sensor with the area 1 mm2 is p = 0.01 bar … 100 barDynamic range limited by nonlinearity and eventually the membrane touching the bottom wafer (=> advantage: tolerance against pressure shocks)

Readout of a capacitive sensor

1. AC readout (i.e., displacement measurement)

∆∆∆∆p ⇒⇒⇒⇒ C →→→→ C+ ∆∆∆∆C ∼∼∼∼

)sin()( 0 tVtV ω=

)sin()()( 0 tIItI ω∆+= )sin(out tV ωG

V 1 MHz, 12/for A 6

)sin( )(For pF1Typically

====

==

AC

ACAC

AC

VCVi

tVtVC

πωµω

ω

Transfer function of the capacitive pressure sensor

0

0.4

0.8

1.2

1.6

0 0.1 0.2 0.3 0.4 0.5 0.6

dxCC

CUi AC

/10

−≈

∆=∆ ω

max/ pp ∆∆

sign

al c

urre

nt ∆

i

2. DC readout (velocity measurement)

Bias the membrane by “constant” charge and measure voltage changes induced by the motion of the membraneVelocity of the diaphragh is measured, NOT positionMotional current (calculate typical example)Examples: microphone, dynamical pressure, vibration, resonators

2p

1p

F = F(t)Ubias

C = C(t)

R

Q= CV = constant over τ = RC

=> ∆V=-Ubias∆C/C

3. Readout using a tuned circuit

IMPROVED RESOLUTION BY TUNING!

Vs RiRloss

CRs

ZC

LRL

MIX LFP

0 deg (I)90 deg (Q)

ref

Q-factor enhancement to the 90 deg signal => high resolutionSqrt(Q) enhancement of the noise at the resonance frequencyLong term stability of the tuned circuit problematic (e.g., T coeff of the inductor)0 deg signal is a measure of the loss factors

Suited particularly for dynamic measurements: dynamic pressure, microphone, vibration, ..

4. Capacitive sensors based on the loss factor measurement

Object to be measured e.g. fingerprint

e.g. matrix of electrodes,of interdigited capacitor

R CC

Vs MIX LFP

0 deg R information90 deg (Q)

ref

5. Resonating capacitive sensors

Advantages over static capacitive sensors

• Improved resolution (at least sometimes)• Easier to make a readout electronics which does not limit the resolution• Output can be coded in the frequency of the output voltage. This may be an advantage.• Several measurements can be measured transformed into a mechanical resonance measurement (strain, force, pressure, acceleration, temperature, mass depostion, ..)• Additional information can be obtained from the dissipation (Q value of the mechanical resonance)

Equation for the mechanical resonance

ηx

m

k

Fext

2

220222

0 )(

1)(

Q

Gωω

ωω

ω

+−

=

ηω /0mQ =

Transfer function at operation point:

00 2 fπω =

extFkxdtdx

dtxdm =++η2

2

Fext = Mechanical force + Electrical force

Motional quantities (“m”)Static capacitance

mBequivn TRkv 4. =

mC

mL

mR0C

.equivmV

.equivnv

mi

Mechanical resonator as a sensor

Spring term: strain, force, pressure, acceleration, ..

Mass term: mass change, pressure, ..

Loss term: pressure from flow loss, viscous surface effects, rapid mass fluctuations, ...

mC

mL

mR0C

.equivmV

.equivnv

mi

Example: resonating pressure sensor (Tomi Mattila et al, 2000)

w=420 µm

L=158 µm

h=5 µm

d=1 µm

Network analyser

Uin

Uout

(a)

(b)

r(µm) 1.0 1.5 2.0 3.0

etch holes

-60

-50

-40

-30

-20

-10

364200 364300 364400 364500Frequency (Hz)

Uou

t/Uin

(dB

)-200

-150

-100

-50

0

50

Phas

e (d

eg)

Example: resonating pressure sensor (2)

CmRm Lm

Cw

Uin

Cp

UDC

50 ΩΩΩΩ

100 nF

100 pFCcoaxCin

25 pF50 ΩΩΩΩ

Uout

0.001 0.01 0.1 1 10p (mbar)

Dam

ping

fact

or r

(Ns/

m) a = 1.0 µµµµm

a = 1.5 µµµµma = 2.0 µµµµma = 3.0 µµµµm

10-5

10-9

10-6

10-7

10-8

Measurement techniques related to capacitive sensors

Dynamical range of AC readout

∆∆∆∆p ⇒⇒⇒⇒ C →→→→ C+ ∆∆∆∆C ∼∼∼∼

)sin()( 0 tVtV ω=

)sin()()( 0 tIItI ω∆+= )sin(out tV ω

n

out

GVV max

best At

G

Background current limits dynamical range

Bridge measurement

∆∆∆∆p ⇒⇒⇒⇒ C →→→→ C+ ∆∆∆∆C ∼∼∼∼

)sin()( 0 tVtV ω=

)sin(out tV ωG

-1

• Zero background signal• Improved dynamical range• Reference C on the same chip!• Stability requirement on the source relieved

• Resolution NOT improved• Inverter should be stable!

Guarding of parasitic capacitances

Intrinsic parasitic C(cannot be bootstrapped)(f.ex. anchor area ofreleased MEMS)

Parasitics from cables, f.ex.(CAN be guarded)

(active) guardingbootstrapping

Guarding of parasitic capacitances (2)

The potential of the signal line is keptat virtual ground => no current flowsacross Cp

Force feedback

∆∆∆∆p ⇒⇒⇒⇒ Vfb→→→→ Vfb + ∆∆∆∆Vfb

∼∼∼∼

)sin(out tV ωG

-1

Electrostatic force

Feedback controller

2

2

2dAVFe

ε=

Features of force feadback

Nonlinearity of the spring does not matter since the membrane is not moving

Linearity requirement now concerns the feedback circuitry, not the transducer

Obtaining linearity requires special solutions since electrostatic force is proportional to the voltage squared

Transfer function is modified by the feedback

Micromechanical silicon precision scale

Exploded view

Electrodes

Contact pad

SpringSOI chip

Glass base

Metallization (Al)

Top view

VTT Automation, VTT Electronics, MIKES

(First) prototype electronics for the precision scale

Ze

Preamplifier

OSC600kHz L P L F

SQRT-1

+1

RF-amplifier

G

PI

Scale

DVM

Reference

0, 1

1

1 0

dC/C

(ppm)

0, 1

1

1 0

dC/C

(ppm)

Brownian Noise of Capacitive Sensors

DYNAMICS OF MEMS CAPACITOR

( ) ( ) nmechn FFVVxd

Akxdtdx

dtxdm +++

−=++ 2

22

2

2εη

mechF is a mechanical force (f.ex., gravity)

nV is the voltage noise )(2)()( τδτ TRktVtV Bnn =+

nF is the force noise )(2)()( τηδτ TktFtF Bnn =+

• Nonlinear dynamics (=> mixing effects)

• Coupling between electrical and mechanical

noise

From friction to noise

Linearized system: ωω ω fGx )(=

Transfer function Qi

kG/

/)(0

220

20

ωωωωωω

+−= ,

mk=0ω

Thermal noise

( ) ( )

hyvyysluku mekaaninenon , in,kitkakerroon

4

42/

21

21

0

2

2

402

02

0

2220

40

2

22

2

2

QQ

kTkf

kTk

kQfd

Qkfx

xkTk

Bn

Bn

nn

nB

ωηη

η

ωπω

ωωωωω

=

=

==+−

=

=

∫∞

Brownin liike

(White force noise assumed)

Q=100

Q=10

1,0E-10

1,0E-09

1,0E-08

1,0E-07

1,0E-06

0,1 1 10

√xn2 /d

2 (1

/√H

z)

0/ωω

Q=100

Q=10

Displacement noise

Low-freq noise decreases by increasing Q (= decreasing friction)(vacuum encapsulation)

Mechanical noise

measω

0at 4

at 4/

20

20

22

==

==∆

ωω

ωωω

kdQTk

kdTQk

fdx

B

mBn

Signal-to-noise

-10

-5

0

5

10

0,1 1 10

Q=100

Q=10

( ) ( )

kd

fQd

x ωω

ωωωω

ωω Re//1

/1Re2

022

02

20

2

+−

−=

0/ωωat low frequencies

fTk

Fk

Q

dxdx

NS

B

n

∆=

=

4

//

0

22

ω

dx /Re ω

Other noise sources!

Intrinsic only!

Q=100

Signal-to-noise is the important quantityNot signal itself (i.e. sensitivity)

Capacitive sensor has an internal noise mechanism which arises from internal energy dissipation.

It is temperature dependent.

It can be quantitatively predicted !

Magnitude of the noise can be calculated from the equipartiontheorem ½ kx2 = ½ kBT and the equation of motion for the released membrane of the capacitive sensor.

The latter determines how noise is shaped with frequency.

Electrostatic actuation (the concept of transducer)

Actuation (i.e. movement) of the released electrode by using electrostatic force

x

U=0

U=V

d-x

springel FF = <=> kxxd

AV=

− 2

20

)(2ε

Pull in at 0

2

278

CkdV pi =

The electrodes are snapped together due to the nonlinearity of the electrostatic force

“Eigencurve” of a moving parallel plate capacitor

0

0,2

0,4

0,6

0,8

1

1,2

0 0,2 0,4 0,6 0,8 1

V/V

pi

δV2

δV1

δx/d1 δx/d2

Stabilize this point and measure the voltage

maxmax /or /by controlled / QQiidx ACAC

CV curve of a moving plate capacitor

-8 -6 -4 -2 0 2 4 6 8

4

5

6

7

8

9

C

(pF)

UDC (V)

• CV curve shows that the sensor is working• Can be used for self test

MiscellaneousLiterature1. Stanfordin tämään kevään “Introduction to Sensors” kurssi

http://design.stanford.edu/Courses/me220/me220.html 2. M. Elwenspoek, R. Wiegerink: “Mechanical Microsensors” ,

Springer 2001 (contains no S/N analysis!!!)3. Universal capacitive readout (= general purpose ultra-low noise

CMOS ASIC, contact info@microsensors.com)4. Y. Netzer, “The Design of Low-Noise Amplifiers”, Proc. IEEE

Vol. 69, No. 6, p. 728 – 741 (1981).

http://design.stanford.edu/Courses/me220/list.html#notes

Lecture 1: Human/Animal Sensors Lecture 2: Sensor Performance Characteristics Lecture 3: Strain Gauges Lecture 4: Capacitive Sensors and Accelerometer Fundamentals Lecture 5: ADXL50 Micromachine Accelerometer Demonstration Lecture 6: Piezoelectric Sensors Lecture 7: Pressure Sensors Lecture 8: Thermometers Lecture 9: Flow Sensors Lecture 10: Radiation Sensors Lecture 11: IR Sensors Demo: IR Motion Lecture 12: Inductive and Magnetic Sensors Lecture 13: Active Sounding Measurement Techniques ExamplesLecture 14: DC Motor Demonstration Lecture 15: Micromachine Sensor Design and Fabrication Lecture 16: Chemical Sensors

Lecture 17: Gyroscopes

Other (RF) MEMS coursess

• Prof. Antti Räisäsen RF-MEMS kurssi• International master’s program on RFMEMS through the AMICOM

Network of Excellence (Advanced MEMS for communications)• VTT is a partner is this network• Contact persons: jussi.tuovinen@vtt.fi, aarne.oja@vtt.fi