Post on 08-Mar-2018
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