Capacitive sensors and their readout electronics

Capacitive sensors and their readout electronics Aarne Oja VTT Information Technology Microsensing [email protected]

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 p2

(

F = ( p2 − p1 ) A = kx

)

3 1 −ν 2 ∆pR 4 x= Et 3 16 x advantage: tolerance against pressure shocks)

Readout of a capacitive sensor 1. AC readout (i.e., displacement measurement)

V (t ) = V0 sin(ωt )

Typically C = 1 pF For V (t ) = V AC sin(ωt ) i AC = ωV AC C = 6 µA for ω / 2π = 1 MHz, VAC = 1 V

∼

∆p ⇒ C → C+ ∆C I (t ) = ( I 0 + ∆I ) sin(ωt )

G

Vout sin(ωt )

Transfer function of the capacitive pressure sensor

∆i = ω∆CU AC C0 C≈ 1− x / d signal current ∆i

1.6 1.2 0.8 0.4 0 0

0.1

0.2

0.3

∆p / ∆pmax

0.4

0.5

0.6

2. DC readout (velocity measurement)

Ubias

p2 F = F(t)

R C = C(t)

Q= CV = constant over τ = RC p1 => ∆V=-Ubias∆C/C Bias the membrane by “constant” charge and measure voltage changes induced by the motion of the membrane Velocity of the diaphragh is measured, NOT position Motional current (calculate typical example) Examples: microphone, dynamical pressure, vibration, resonators

3. Readout using a tuned circuit IMPROVED RESOLUTION BY TUNING!

Rs

C

RL

L MIX LFP

Vs

Rloss ZC

Ri

ref 0 deg (I) 90 deg (Q)

Q-factor enhancement to the 90 deg signal => high resolution Sqrt(Q) enhancement of the noise at the resonance frequency Long 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 C

Vs

R

C

e.g. fingerprint e.g. matrix of electrodes, of interdigited capacitor MIX LFP ref

0 deg R information 90 deg (Q)

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 d 2x dx m 2 + η + kx = Fext dt dt

Fext = Mechanical force + Electrical force

Fext

Transfer function at operation point:

Vmequiv.

k

(ω − ω ) + 2 0

m x

η

1

G (ω ) =

Cm

2 2

ω0 = 2πf 0

ω 02ω 2 Q2

Q = ω 0 m /η

Lm Static capacitance C0

Rm

v

equiv . n

im

Motional quantities (“m”) vnequiv. = 4k BTRm

Mechanical resonator as a sensor Vmequiv. Cm Lm C0

Rm

vnequiv.

im

Spring term: strain, force, pressure, acceleration, .. Mass term: mass change, pressure, .. Loss term: pressure from flow loss, viscous surface effects, rapid mass fluctuations, ...

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

etch holes

Uin -10

50

-20

0

-30

-50

-40

-100

-50

-150

(a)

Network analyser w=420 µm L=158 µm

Uout

Uout/Uin (dB)

d=1 µm

-60 364200

364300

364400

Frequency (Hz)

(b) r(µm)

1.0

1.5

2.0

3.0

-200 364500

Phase (deg)

h=5 µm

Example: resonating pressure sensor (2)

-5

Cm

100 nF

10

Lm

Cw

50 Ω

Cp Uout

UDC

Uin

50 Ω

Cin

Ccoax

25 pF

100 pF

Damping factor r (Ns/m)

Rm

-6

10

a a a a

= 1.0 µm = 1.5 µm = 2.0 µm = 3.0 µm

-7

10

-8

10

-9

10

0.001

0.01

0.1

p (mbar)

1

10

Measurement techniques related to capacitive sensors

Dynamical range of AC readout

V (t ) = V0 sin(ωt )

∼

max Vout At best GVn

Background current limits dynamical range

∆p ⇒ C → C+ ∆C I (t ) = ( I 0 + ∆I ) sin(ωt )

G

Vout sin(ωt )

Bridge measurement

V (t ) = V0 sin(ωt )

∼

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

∆p ⇒ C → C+ ∆C

G

-1

Vout sin(ωt )

• Resolution NOT improved • Inverter should be stable!

Guarding of parasitic capacitances

(active) guarding bootstrapping

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

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

Guarding of parasitic capacitances (2)

The potential of the signal line is kept at virtual ground => no current flows across Cp

Force feedback

Electrostatic force

∆p ⇒ Vfb→ Vfb + ∆Vfb

Fe =

εAV 2 2d 2

Feedback controller

∼

G

-1

Vout sin(ωt )

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

Top view Metallization (Al) SOI chip

Spring Electrodes

Glass base

Contact pad

VTT Automation, VTT Electronics, MIKES

(First) prototype electronics for the precision scale

SQRT 0

)( m p

1

, 0

1

PI

C /

1

d

-1 Preamplifier Reference OSC 600 kHz

RF-amplifier

Scale

G

DVM +1

Ze

LP

LF

Brownian Noise of Capacitive Sensors DYNAMICS OF MEMS CAPACITOR

d 2x dx εA 2 ( ) m 2 + η + kx = V + V + Fmech + Fn n 2 dt dt 2(d − x ) Fmech is a mechanical force (f.ex., gravity) Vn is the voltage noise Vn (t )Vn (t + τ ) = 2k BTRδ (τ ) Fn is the force noise Fn (t ) Fn (t + τ ) = 2k BTηδ (τ )

•

Nonlinear dynamics (=> mixing effects)

•

Coupling between electrical and mechanical noise

From friction to noise Linearized system: xω = G (ω ) fω

ω 02 / k Transfer function G (ω ) = 2 , ω 0 − ω 2 + iω 0 ω / Q k m Thermal noise 1 1 k BT = k xn2 2 2

ω0 =

f n2 x = 2 k 2 n

∞

4 dω k BT 2 ω0 Q f = = n 2 2 k 4k 2 ω 02 − ω 2 + ω 0 2 ω / Q 2π

∫( 0

Brownin liike ω 04

) (

f n2 = 4k BTη

η on kitkakerroin, η =

)

(White force noise assumed)

k , Q on mekaaninen hyvyysluku Qω 0

Mechanical noise Displacement noise xn2 / d 2 4Qk BT = at ω = ω m 2 ∆f ω 0 kd 4 k BT = at ω = 0 2 Qω 0 kd

√xn2/d2 (1/√ Hz)

1,0E-06

Q=100

1,0E-07

ω meas

Q=100 Q=10

1,0E-08

Q=10

1,0E-09 1,0E-10 0,1

1

ω / ω0

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

10

Signal-to-noise

Re{xω } = 2 2 2 d 1 − ω / ω0 + ω / ω0 Q

Intrinsic only!

S = N

x/d 2 n

x /d

(

10 2

Qω 0 F k = 4k BT∆f at low frequencies

) (

Re{xω }/ d

)

2

Re{ fω } kd

Q=100

5

Q=10 0 -5 -10 0,1

Other noise sources!

1 − ω 2 / ω 02

1

ω / ω0

10

Signal-to-noise is the important quantity Not 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 equipartion theorem 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 F el = F spring

ε 0 AV



2

2( d − x )

x

2

= kx

U=V

d-x U=0 Pull in at

V pi =

8 kd 2 27 C 0

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

“Eigencurve” of a moving parallel plate capacitor 1,2 δ V2 1 δ V1

V /V p i

0,8 0,6

Stabilize this point and measure the voltage

0,4 0,2

δ x/d2

δx/d1

0 0

0,2

0,4

0,6

0,8

max x / d controlledby iAC / iAC or Q / Qmax

1

CV curve of a moving plate capacitor 9

8

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

C (pF)

7

6

5

4 -8

-6

-4

-2

0

UDC (V)

2

4

6

8

Miscellaneous

Literature 1. 2. 3. 4.

Stanfordin tämään kevään “Introduction to Sensors” kurssi http://design.stanford.edu/Courses/me220/me220.html M. Elwenspoek, R. Wiegerink: “Mechanical Microsensors” , Springer 2001 (contains no S/N analysis!!!) Universal capacitive readout (= general purpose ultra-low noise CMOS ASIC, contact [email protected]) 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 Examples Lecture 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: [email protected], [email protected]