M. C. Wu 1 EE M250B / MAE M282 / BME M250B

Piezoelectric Transducers

Reference:

• Senturia’s Book: Chapter 21• Maluf, An Introduction to MEMS Engineering, pp. 31-35

M. C. Wu 2 EE M250B / MAE M282 / BME M250B

Piezoelectricity:Coupling between Internal Dielectric Polarization and Strain

• Piezoelectric crystals – Produce electric field when subject to an external force– Expand or contract in response to externally applied

voltage• Can be used for both sensors and actuators• Piezoelectric effect discovered in 1880• Macroscale piezoelectric actuators widely used in many

applications• Large force, low power consumption

– A few Newtons in bulk piezoceramic cylinders– A few millinewtons in thin films

• Hysteresis, drift, nonlinearity ���� Often placed in a feedback loop

• Microscale piezoelectric thin film materials for MEMS applications are still challenging

• Piezoresitive materials are usually not piezoelectric

M. C. Wu 3 EE M250B / MAE M282 / BME M250B

Does Si Exhibit Piezoelectric Effect?

• Si is not piezoelectric– Cubic, has a center of symmetry– Covalent bond (not ionic)

• Crystals with a center of symmetry does not have piezoelectric effect

• The electric dipoles always add up to zero

M. C. Wu 4 EE M250B / MAE M282 / BME M250B

Piezoelectric Crystal

• Necessary conditions:– Ionic or partly ionic bonds– Lack a center of symmetry

• Strain shifts the relative positions of the positive and negative charges, giving rise to a net electric dipole

• Conversely, electrical field ���� strain

M. C. Wu 5 EE M250B / MAE M282 / BME M250B

Illustration of Piezoelectric Effect

PED += 0ε

Electric FieldPolarization (function of strain)

Permittivity of free spaceElectric Displacement

Electrostatic Energy Density: EDWe ⋅=21ˆ

eW is a function of strain since P is a function of strain

StressWe →∂

∂εˆ

���� Actuation Force

M. C. Wu 6 EE M250B / MAE M282 / BME M250B

Analytic Formulation for Piezoelectricity

∑∑

∑∑

==

==

+=

+=

3

1

6

1

3

1

6

1

jjij

JJiJi

jjIj

JJIJI

EdD

dES

σ

ε

εσ

σε

Strain (column vector with 6 elements)

Compliance Coef

StressElectric Field

Piezoelectric Stress Coef (3x6 array)

Unit: Coul/Newton

Dielectric Tensor

∑∑

∑∑

==

==

+=

+=

3

1

6

1

3

1

6

1

jjij

JJiJi

jjIj

JJIJI

EeD

eEC

ε

ε

εε

εσ

For analyzing actuators

For analyzing vibrations Piezoelectric Coef(3x6 array)

Unit: Coul/meter2

Stiffness Coef

M. C. Wu 7 EE M250B / MAE M282 / BME M250B

Relationship between diJ and eiJ

∑

∑

=

=

=

=

6

1

6

1

KKJiJiJ

KKJiKiJ

Cde

Sed

ε

εPiezoelectric Stress Coef

Piezoelectric Coef

M. C. Wu 8 EE M250B / MAE M282 / BME M250B

Piezoelectric Materials

• Piezoelectric substrates– Quartz, LiNbO3, GaAs

• Thin film piezoelectrics– ZnO, AlN, PZT (lead zicornate-titanate)

• Polymer film piezoelectrics– PVDF (poly-vinylidene flouride)

−−−

=00000020000000

1114

141111

ddddd

dQuartz:

ZnO:

=0000000000000

333131

15

15

eeee

ee

M. C. Wu 9 EE M250B / MAE M282 / BME M250B

Common Piezoelectric Materials

PZT: lead zirconate-titanatePVDF is polymer-film peizoelectrics

M. C. Wu 10 EE M250B / MAE M282 / BME M250B

Piezoelectric Actuation

a

a

a

Vdtt

WVdW

tLVdL

31

31

31

=∆

=∆

=∆

If a voltage is applied in the thickness direction���� Strain occurs in length, width, and thickness directions

M. C. Wu 11 EE M250B / MAE M282 / BME M250B

Piezoelectric Sensing

LWtFdV

WFdV

LFdV

m

m

m

εεεε

εεεε

εεεε

33

31

31

=

=

=

Force F is applied in L, W, or t direction�A voltage will develop�Can be used for sensors

M. C. Wu 12 EE M250B / MAE M282 / BME M250B

Piezoelectric Bimorph

0

0

E3V

A biormorph structure can be used to enhance the displacement