# Piezoelectricity

```Piezoelectricity
• Polarization does not disappear when the electric field
removed.
• The direction of polarization is reversible.
saturation
Polarization
Remenent
polarization
Ps
Pr
+Vc
Voltage
Coercive
voltage
Figure by MIT OCW
FRAM utilize two stable positions.
Sang-Gook Kim, MIT
Figure by MIT OCW
15
Polarization (&micro;C/cm2)
Hysterisis
Electric Field (kV/cm)
Ferroelectric (P-E) hysteresis loop. The circles with arrows indicate the polarization
state of the material for different fields.
Sang-Gook Kim, MIT
Figure by MIT OCW.
16
Domain Polarization
• Poling: 100 C, 60kV/cm, PZT
• Breakdown: 600kV/cm, PZT
• Unimorph cantilever
Sang-Gook Kim, MIT
17
Piezoelectricity
Direct effect
D = Q/A = dT
Converse effect
T = -eE
E = -gT
g = d/ε = d/Kε
S = dE
o
E = -hS
• D: dielectric displacement, electric flux density/unit area
• T: stress, S: strain, E: electric field
• d: Piezoelectric constant, [Coulomb/Newton]
Boundary
Conditions
Free
T
d = (∂S/∂E) = (∂D/∂T)
Short circuit
E
g = (-∂E/∂T) = (∂S/∂D)
Open circuit
D
e = (-∂T/∂E) = (∂D/∂S)
Clamped
S
h = (-∂T/∂D) = (-∂E/∂S)
Sang-Gook Kim, MIT
T
E
D
S
S
T
E
D
18
Principles of piezoelectric
Electric field(E)
Pi
ez
d
d
Strain(S)
-e
g
t
ec
-h
Stress(T) c
Dielectric
Displacement(D)
eff
-e
β
ε
al
rm
oe
lec
tri
ce
ffe
ct
-h
e
-th
tro
ec
El
g
Entropy
s
Temperature
Thermo-elastic effect
Sang-Gook Kim, MIT
19
Equation of State
Basic equation
d-form Sij = sijklETkl+dkijEk
Di = diklTkl+ εikTEk
g-form S = sDT+gD
E = -gT+ βTD
e-form Tij = cijklESkl-ekijEk
Di = ekijSkl+ εikSEk
h-form T = cDS-hD
E = -hS+βSD
Sang-Gook Kim, MIT
cE = 1/sE
e = dcE
εE = εT-dcEdt
βT = 1/εT
g = d/εT
sD = sE-dt(εT)-1d
D = Q/A
S = F/A
20
Equation of states
D = dT + ε E
S = s T + dE
T
E
direct
converse
Tensor to Matrix notation
For cylindrical symmetry, and poling in axis 3,
D =ε E +d T
1
1
1
15
5
3
D = ε E +d T
2
1
2
15
4
D = ε E + d (T + T ) + d T
3
3
3
31
1
2
33
S = s T +s T +s T +d E
3
S = s T +s T +s T +d E
3
1
2
11
11
1
12
2
2
12
13
1
13
3
3
31
31
S = s (T + T ) + s T + d E
S =s T +d E
3
4
13
44
1
4
2
15
S =s T +d E
5
44
5
15
33
3
33
6
3
4
5
2
1
3
2
1
S =s T
6
Sang-Gook Kim, MIT
66
6
21
Applications of piezoelectric
Sensors
Pressure sensors
Accelerometers
Gyroscopes
Power generators
Actuators
Vibrators
Ultrasonic transducers
Resonators / Filters / Switches
Surface Acoustic wave(SAW) devices
Transformers
Actuators
Ultrasonic motors
Sang-Gook Kim, MIT
22
Piezoelectric Charge Constants
Electrical energy
Longitudinal (d33)
Source: Piezo Systems, Inc.
&quot;Introduction to Piezo Transducers.&quot;
http://www.piezo.com/bendedu.html
∆T/T = d33 &middot; E
Sang-Gook Kim, MIT
Actuator
Mechanical energy
Transverse (d31)
Source: Piezo Systems, Inc.
&quot;Introduction to Piezo Transducers.&quot;
http://www.piezo.com/bendedu.html
ΔL/L = d31 &middot; E
Shear (d15)
E
P
Shear strain
= d15 E
23
Piezoelectric Charge Constants
Mechanical energy
Longitudinal (d33)
Source: Piezo Systems, Inc.
&quot;Introduction to Piezo Transducers.&quot;
http://www.piezo.com/bendedu.html
Q = d33 &middot; Fin
Vout/T = g33 &middot; Fin /(L &middot; W)
Sensor
Transverse (d31)
Source: Piezo Systems, Inc.
&quot;Introduction to Piezo Transducers.&quot;
http://www.piezo.com/bendedu.html
Electrical energy
Multi-layer (d33)
Source: Piezo Systems, Inc.
&quot;Introduction to Piezo Transducers&quot;
http://www.piezo.com/bendedu.html
Q = d31 &middot; Fin
Q = n &middot;d33 &middot; Fin
Vout /T= g31 &middot; Fin/(T &middot; W) Vout /T= t/n &middot; g33 &middot; Fin /(LW)
24
Sang-Gook Kim, MIT
d31 vs d33
Homework 2:
Compare generated
voltages V31 (from d31mode),
V33 (d33mode). Both have
same cantilever dimension, but
different electrodes.
d33=200 pC/n
K=1000
Assume, g33=2g31
tpzt=o.5 &micro;
d=5 &micro;
length=100 &micro;, width=50 &micro;
Young’s modulus of the beam=
65 Gpa, max. strain = 0.1%
Interdigitated Electrode
+ - + - + - +
P
PZT layer
ZrO2 layer
Membrane layer
Sang-Gook Kim, MIT
25
Design of a Z-positioner
Component schematic removed for copyright reasons.
Physik Instrumente Z-positioner P-882.10, in
http://www.pi-usa.us/pdf/2004_PICatLowRes_www.pdf, page 1-45.
Ordering Number*
Dimensions
AxBxL
[mm]
Nominal
Displaceme
nt [&micro;m @
100 V]
(&plusmn;10%)
Max.
Displaceme
nt [&micro;m @
120 V]
(&plusmn;10%)
Blocking
Force [N @
120 V]
Stiffness
[N/&micro;m]
Electrical
Capacitance
[&micro;F] (&plusmn;20%)
Resonant
Frequency
[kHz]
P-882.10
2x3x9
7
9
215
26
0.13
135
Sang-Gook Kim, MIT
26
Fabrication Methods for PZT thin Films
Annealing temperature ( o C )
1200
Screen printing
600
Sputtering,
CVD or
Laser ablation
0.02
Sol-gel
Gas-jet
.
deposition
1
100
Film Thickness (um)
Sang-Gook Kim, MIT
27
Sol-Gel spin coating
• Vacuum chamber not necessary (simple)
• Easy composition control
• Deposition on large flat substrate
• Difficult to deposit on deep trenched surface
• Higher raw material consumption
Sang-Gook Kim, MIT
28
PZT film
Unlimited resolution
Large force generation
Fast expansion
No magnetic fields (low cross talk)
Low power consumption
No wear and tear for actuation
Vacuum and clean room compatible
Operation at cryogenic temperature
Sang-Gook Kim, MIT
Complex fabrication
Hysteresis
Life cycle (1012 cycles)
; Fatigue, retention…
29
Typical Layer Structures for
Sol-Gel PZT
Top electrode Pt (e-beam evaporation lift-off)
Piezoelectric PZT (sol-gel spinning)
Bottom electrode Pt/Ti (e-beam evaporation lift-off)
Diffusion barrier SiO2 or SiNx (CVD)
Diffusion barrier ZrO2(sol-gel spinning)
Si substrate
d31 mode
Sang-Gook Kim, MIT
Si substrate
d33 mode
30
Thermal Oxide Growth and Bottom Electrode Evaporation
Tubes for growing of
device diffusion barrier
Evaporation of
device electrodes
Sang-Gook Kim, MIT
Photos: MIT Microsystems Technologies Laboratory
31
Fabrication of the PZT Film
PZT Sol material
18% PbO excess PZT (52/48)
Spin coating
At 500 rpm for 3sec
and at 3000 rpm for 30sec
Drying
At 350&deg;C for 5 min. (hot plate)
Annealing
At 650&deg;C for 15 min. (box furnace)
Wet etching
HCl(64%)+BOE(31%)+DI (5%)
(0.25 &micro;m/min)
Spin-coat Mitsubishi PZT sol-gel: 15% PZT(118/52/48) A6 Type
Sang-Gook Kim, MIT
32
Fabrication of the PZT Film
PZT Sol material
Spin coater
PZT sol
Spin coating
Drying
Annealing
Wet etching
Sang-Gook Kim, MIT
Annealing furnace
Photo: MIT Microsystems Technologies Laboratory
33
PZT Patterning
Patterned PZT on device
PZT
PZT
bottom electrode
cantilever
bottom electrode
gratings
top electrode
thin-film PZT
bottom electrode
Sang-Gook Kim, MIT
34
PZT Patterning (Wet ethcing)
PZT wet-etching with thick photoresist
photoresist
PZT film
Membrane and eletrode
Silicon substrate
5 &micro;m photoresist
688 nm
256 nm
PZT layer
Pt/Ta layer
silicon substrate
Sang-Gook Kim, MIT
HCl(64%)+BOE(31%)+DI (5%)
(etch rate: 0.25 &micro;m/min) 35
PZT Patterning (Wet ethcing)
PZT wet-etching with thin resist
photoresist
PZT film
Membrane and eletrode
Silicon substrate
photoresist
residual PZT
open region
• large undercuts with thin (1 &micro;m) photoresist material
1 W. Liu et al, Thin Solid Films, 2000.
2
K. Yamashita et al,Transducers ‘01, Munich.
Sang-Gook Kim, MIT
36
PZT Patterning (Dry etching)
PZT dry-etching with thick resist
photoresist
PZT film
Membrane and eletrode
Silicon substrate
using RIE, Plamaquest (in TRL) or Plasmatherm (in EML)
with BCl3:Cl2 (30:10)
• stiff sidewall with thick (10 &micro;m) photoresist
material
Sang-Gook Kim, MIT
37
Top Electrode Lift-Off
cantilever
doubly-hinged membrane
d33 mode interdigitated structure
bottom electrode
top electrode
perforated membrane
thin-film
PZT
PZT undercut
close-up on multi-layers
100 um
d31 mode sandwich structure
Pt/Ti top electrode pattern by lift-off, 220
nm thick.
Sang-Gook Kim, MIT
38
Micro-structure of PZT Thin Film
SEM of PZT film surface
Average grain size : 0.1&micro;m
Cross sectional image of PZT film
PZT thickness = 510 &plusmn; 40 nm;
Pt thickness = 200 nm.
Using SEM
Sang-Gook Kim, MIT
39
PZT XRD On Various Bottom Electrode
Combinations
Pt(111)
PZT/Pt/Ti/SiNx - no hillocks
PZT(011)
PZT(111)
Intensity (A.U.)
PZT(001)
PZT(002)
CuKβ
PZT(102)
Pt(002)
PZT(112)
PZT/Pt/Ti/SiO2 - no hillocks
Pyrochlore
PZT/Pt(annealed)/Ta/SiO2 - a few hillocks
Pyrochlore
PZT/Pt(no annealed)/Ta/SiO2 - many hillocks
WLα
20
30
40
50
60
Using XRD
2θ
Sang-Gook Kim, MIT
40
Electrical Measurements - PZT Ferroelectric
Characterization
80
2
Polarization (&micro;C/cm )
60
Ps
40
20
0
2Pr
-20
2
Area:260x260 &micro;m
ε =1172, tanδ=0.04
2
Ps=65&micro;C/cm
-40
2
2Pr=50&micro;C/cm
Vc=3V (Ec=60KV/cm)
-60
Vc
-80
-20
-15
-10
-5
0
5
10
15
20
Using RT-66A
Applied voltage (V)
• hysteresis due to domain reorientation - growth, merging and
shrinkage
• saturation polarization, Ps at 65 &micro;C/cm2
• remnant polarization, 2Pr at 50 &micro; C/cm2
Sang-Gook Kim, MIT
41
Percentage change from initial
value
Piezoelectric Fatigue Analysis
120
PZT characteristics against number of cycles
1.5E10 cycles
100
80
3.1E10 cycles
60
40
20
3.9E10 cycles
1st run
2nd run
5V-19.6&micro;s-rectangular pulse-train
dons-d14F
0
1.E+04
1.E+06
1.E+08
1.E+10
1.E+12 Using RT-66A
fatigue cycles
• PZT electrical fatigue up to more than 1E10 cycles
• characteristics recovered on 2nd run with same device
Sang-Gook Kim, MIT
42
Piezoelectric Displacement Analysis
Estimated membrane strain (%)
0.035
Saturation voltage ~ +/- 15V
0.03
0.025
0.02
0.015
measurement
0.01
corresponding
0.005 predictions
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
Applied voltage (V)
strain = d31V/t
1
direct measurement
Sang-Gook Kim, MIT
(d33=275pC/N 1, d31=-115pC/N 2)
2
inferred from mechanical motion
Using computer microvision system
43
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