Practical MEMS

Chapter 3: Accelerometers

http://www.kaajakari.net/PracticalMEMS

Micromachined accelerometers

• The “second” MEMS product (first was pressure sensors).• Applications:

– Crash detectors for air bag deployment. Over 6,000 lives saved in US.– Low-G sensors are used for active suspensions and vehicle stabilization

controls. – Motion based user interfaces (e.g. game consoles, cell phones)– Step counters, running speed and distance.– Digital cameras to determine the picture orientation.– Free fall detection to protect laptop hard drives

Principle of operation

• A proof mass is attached to frame with a spring.

• When the frame is accelerated, the proof mass follows the frame motion with a lag.

mk

γ

mx

fx

Frequency response

mk

γ

mx

fxmf xxx −=

fxmkxtx

txm &&=+

∂∂

+∂∂ γ2

2

ksmsxm

x f

++=

γ2

&&

Equation of motion:

The proof mass displacement relative to the frame is proportional to the acceleration!

Amplitude of the response

20ωff x

kxm

x&&&&

=≈ ff xx

x =≈ 2ω&&

2

0

2

2

2

0

1

/

+

−

=

ωω

ωω

Q

kxmx f&&

wheremk

=0ω andγ

ω mQ 0=

|x|

Excitation frequency

low frequency response

high frequency response

Changing the resonant frequency

•Lowering ω0 improves low frequency response but does not affect high frequency response.

•Overall, lowering ω0 helps.•Taken to extreme ω0 = 1-2 Hz! (Macroscopic seismometers).

•For MEMS typically ω0 > 50 HZ.

100 101 102 103 10410-9

10-8

10-7

10-6

10-5

10-4

Frequency[Hz]

|X|

Scaling laws for accelerometers

What happens when all dimensions are reduced 10x?

mk

γ

mx

fx

fmf xkmxx &&=−

100

10

000,1

mfmf

xxxx

kk

mm

−→−

→

→

(Analog devices accelerometers measure 0.1 Å displacements!)

0 2 4 60

0.5

1

1.5

t⋅f0

x[F/

k]

Q = 0.5

Q = 0.2

Q = 2

Time domain response

Critical damping or over damping preferred for clean response

Sensing principles

• Piezoresistive– Stress sensitive resistors integrated in the springs– Robust– Noisy, high power, and large temperature dependency

• Capacitive– Direct measurement of displacement– Low power, low noise– Small capacitance measurement is difficult

• Piezoelectric– Self generating– Signal proportional to change in stress – no dc signal!

• Magnetic• Optical

mk

γ

mx

fx [ ]Hz/m/s4

:onaccelerati equivalent Noise

20

mQTkx B

nω

=&&

Noise equivalent acceleration(spectral density)

xmFTkF

x

Bn

&&&& =

= γ4

:forceon acceleratiapparent andgenerator force noise Equate

mk

γ

mx

fx

Noise equivalent acceleration(rms acceleration)

kTkx

Tkkx

B

B

=⇔

=

2rms

2rms 2

121

fmf xkmxxx &&=−=

mTk

mTkkx BB

20

2rms

ω==&&

Total rms noise depends only on mass and resonant frequency!

(1)

(2)

A2 =1k

A1 = m

F n =√4kBTγ

x xF

System level noise model

C1C2

anchorfolded spring

proof mass

Quality factor

Electrode capacitance

Spring constant

Mass

Resonant frequency

Parameter

3-4Q

pF0.1C0

N/m2k

nkg0.1m

kHz22f0

UnitsValueSymbol

APPLIED ACCELERATION

TOP VIEWTOP VIEW

MASS

SPRING

DENOTES ANCHOR

FIXED SENSING FINGERS

C1C2

C1C2

MASS

Surface micromachined accelerometer

HzmG/2.0=nx&&

ADXL50 Accelerometer• +/-50G• Polysilicon MEMS &

BiCMOS• 3x3mm die

1000 µm

Quality factor

Electrode capacitance

Spring constant

Mass

Resonant frequency

Parameter

0.1Q

pF5C0

N/m50k

µkg1m

kHz1f0

UnitsValueSymbol

380 µm

proof masselectrode

electrode

Bulk micromachined accelerometer

HzG/3

:onacceleratiequivalentNoise

µ=nx&&