Piezoelectricity

• Polarization does not disappear when the electric field removed. • The direction of polarization is reversible.

Polarization saturation Ps Remenent polarization Pr

+Vc Voltage Coercive voltage

Figure by MIT OCW FRAM utilize two stable positions. Figure by MIT OCW 15 Sang-Gook Kim, MIT Hysterisis ) 2 m c / C µ (

n o i t a z i r a l o P

Electric Field (kV/cm)

Ferroelectric (P-E) hysteresis loop. The circles with arrows indicate the polarization state of the material for different fields.

16 Sang-Gook Kim, MIT Figure by MIT OCW. Domain Polarization

• Poling: 100 C, 60kV/cm, PZT

• Breakdown: 600kV/cm, PZT

•Unimorphcantilever

Sang-Gook Kim, MIT 17 Piezoelectricity

Direct effect D = Q/A = dT E = -gT T = -eE Converse effect E = -hS S = dE g = d/ε = d/Kε o

• D: dielectric displacement, electric flux density/unit area • T: stress, S: strain, E: electric field • d: Piezoelectric constant, [Coulomb/Newton]

Free T d = (∂S/∂E) T = (∂D/∂T) E Boundary Conditions Short circuit E g = (-∂E/∂T) D = (∂S/∂D) T

Open circuit D e = (-∂T/∂E)S = (∂D/∂S) E h = (-∂T/∂D) = (-∂E/∂S) Clamped S S D Sang-Gook Kim, MIT 18 Principles of piezoelectric

Electric field(E)

g β Ele -h c tr ct ε o fe - f th e e c r ri Dielectric m t a Displacement(D) l ec e el f o d fe -e c iez d t P g -e Strain(S) Entropy -h s Stress(T) c Temperature Thermo-elastic effect

Sang-Gook Kim, MIT 19 Equation of State

Basic equation

E d-form Sij = sijkl Tkl+dkijEk cE = 1/sE T E Di = diklTkl+ εik Ek e = dc g-form S = sDT+gD E T E ε = ε -dc dt T E = -gT+ β D βT = 1/εT E T e-form Tij = cijkl Skl-ekijEk g = d/ε D = e S + ε SE D E T -1 i kij kl ik k s = s -dt(ε ) d h-form T = cDS-hD D = Q/A E = -hS+βSD S = F/A

Sang-Gook Kim, MIT 20 Equation of states

D = dT + ε T E S = s ET + dE direct converse Tensor to Matrix notation For cylindrical symmetry, and poling in axis 3,

D1 = ε1 E1 + d15T5 3 D 2 = ε1 E 2 + d15T4 D = ε E + d (T + T ) + d T 3 3 3 31 1 2 33 3 6 S = s T + s T + s T + d E 2 1 11 1 12 2 13 3 31 3 5 4

S2 = s11T2 + s12T1 + s13T3 + d 31 E 3 1 S3 = s13 (T1 + T2 ) + s33T3 + d 33 E 3

S4 = s 44T4 + d15 E 2

S5 = s 44T5 + d15 E1

S6 = s66T6

Sang-Gook Kim, MIT 21 Applications of piezoelectric

Pressure sensors Sensors Accelerometers Gyroscopes Power generators Vibrators Ultrasonic transducers Resonators / Filters / Switches Actuators Surface Acoustic wave(SAW) devices Transformers Actuators Ultrasonic motors

Sang-Gook Kim, MIT 22 Piezoelectric Charge Constants

Electrical energyActuator Mechanical energy

Longitudinal (d33) Transverse (d31) Shear (d15)

Diagram removed for copyright reasons. Diagram removed for copyright reasons. Source: Piezo Systems, Inc. Source: Piezo Systems, Inc. "Introduction to Piezo Transducers." "Introduction to Piezo Transducers." E P http://www.piezo.com/bendedu.html http://www.piezo.com/bendedu.html

ΔL/L = d31 ·E Shear strain ∆T/T = d33 ·E = d15 E

Sang-Gook Kim, MIT 23 Piezoelectric Charge Constants

Mechanical energySensor Electrical energy

Longitudinal (d33) Transverse (d31) Multi-layer (d33)

Diagram removed for copyright reasons. Diagram removed for copyright reasons. Diagram removed for copyright reasons. Source: Piezo Systems, Inc. Source: Piezo Systems, Inc. Source: Piezo Systems, Inc. "Introduction to Piezo Transducers." "Introduction to Piezo Transducers." http://www.piezo.com/bendedu.html "Introduction to Piezo Transducers" http://www.piezo.com/bendedu.html http://www.piezo.com/bendedu.html

Q = d ·F Q = d33 ·Fin 31 in Q = n ·d33 ·Fin Vout/T = g33 ·Fin /(L · W) Vout /T= g31 ·Fin/(T · W) Vout /T= t/n · g33 ·Fin /(LW)

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. Assume, g33=2g31 tpzt=o.5 µ d=5 µ d33=200 pC/n length=100 µ, width=50 µ K=1000 Young’s modulus of the beam= 65 Gpa, max. strain = 0.1%

Interdigitated Electrode + - + - + - + PZT layer P

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 Nominal Max. Blocking Stiffness Electrical Resonant A x B x L Displaceme Displaceme Force [N @ [N/µm] Capacitance Frequency [mm] nt [µm @ nt [µm @ 120 V] [µF] (±20%) [kHz] 100 V] 120 V] (±10%) (±10%)

P-882.10 2 x 3 x 9 7 9 215 26 0.13 135

Sang-Gook Kim, MIT 26 Fabrication Methods for PZT thin Films

1200

) C

o Screen printing

(

a r

e Sputtering, p 600 Sol-gel

m CVD or Gas-jet

e .

t Laser ablation deposition

n A

0.02 1 100 Film Thickness (um)

Sang-Gook Kim, MIT 27 Sol-Gel spin coating

Advantages • Vacuum chamber not necessary (simple) • Easy composition control • Deposition on large flat substrate

Disadvantages • Difficult to deposit on deep trenched surface • Higher raw material consumption

Sang-Gook Kim, MIT 28 Advantage and disadvantage of PZT film

Advantage Disadvantage Unlimited resolution Complex fabrication Large force generation Hysteresis Fast expansion Life cycle (1012 cycles) No magnetic fields (low cross talk) ; Fatigue, retention… Low power consumption No wear and tear for actuation Vacuum and clean room compatible Operation at cryogenic temperature

Sang-Gook Kim, MIT 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 Si substrate

d31 mode d33 mode Sang-Gook Kim, MIT 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)

At 500 rpm for 3sec Spin coating and at 3000 rpm for 30sec

Drying At 350°C for 5 min. (hot plate)

Annealing At 650°C for 15 min. (box furnace)

HCl(64%)+BOE(31%)+DI (5%) Wet etching (0.25 µm/min)

Spin-coat Mitsubishi PZT sol-gel: 15% PZT(118/52/48) A6 Type

Sang-Gook Kim, MIT 32 Fabrication of the PZT Film

Spin coater PZT Sol material PZT sol

Spin coating

Drying

Annealing

Wet etching Annealing furnace

Sang-Gook Kim, MIT Photo: MIT Microsystems Technologies Laboratory 33 PZT Patterning

Patterned PZT on device

PZT PZT

bottom electrode bottom electrode cantilever 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 µm photoresist 688 nm

256 nm PZT layer Pt/Ta layer

silicon substrate

HCl(64%)+BOE(31%)+DI (5%) (etch rate: 0.25 µm/min) Sang-Gook Kim, MIT 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 µm) 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 µm) photoresist material

Sang-Gook Kim, MIT 37 Top Electrode Lift-Off

cantilever

doubly-hinged membrane d33 mode interdigitated structure bottom electrode top electrode

thin-filmperforated PZT membrane

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 Cross sectional image of PZT film

Average grain size : 0.1µm PZT thickness = 510 ± 40 nm; Pt thickness = 200 nm.

Using SEM

Sang-Gook Kim, MIT 39 PZT XRD On Various Bottom Electrode Combinations

Pt(111)

PZT(011) PZT/Pt/Ti/SiNx - no hillocks

PZT(111) PZT(112) PZT(001) PZT(002) PZT(102)

Cu Kβ Pt(002) PZT/Pt/Ti/SiO2 - no hillocks

Pyrochlore PZT/Pt(annealed)/Ta/SiO2 - a few hillocks Intensity (A.U.) Intensity

Pyrochlore PZT/Pt(no annealed)/Ta/SiO2 - many hillocks W Lα

20 30 40 50 60 Using XRD 2θ Sang-Gook Kim, MIT 40 Electrical Measurements - PZT Ferroelectric Characterization 80 P 60 s

) 40 2

20 C/cm µ 0 2P r -20 2 Area:260x260 µm ε =1172, tanδ=0.04 -40 2 P =65µC/cm s 2 Polarization ( Polarization 2P =50µC/cm -60 r V =3V (E =60KV/cm) V c c -80 c -20 -15 -10 -5 0 5 10 15 20 Using RT-66A Applied voltage (V) • hysteresis due to domain reorientation - growth, merging and shrinkage 2 • saturation polarization, Ps at 65 µC/cm 2 • remnant polarization, 2Pr at 50 µ C/cm Sang-Gook Kim, MIT 41 Piezoelectric Fatigue Analysis

PZT characteristics against number of cycles 120

100 1.5E10 cycles

80 3.1E10 cycles 60 value

40 1st run 3.9E10 cycles 2nd run 20 5V-19.6µs-rectangular pulse-train

Percentage initial change from 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

0.035 Saturation voltage ~ +/- 15V

) 0.03

0.025

0.02

0.015

0.01 measurement corresponding 0.005 predictions

Estimated membrane strain (% membrane strain Estimated 0 -10-8-6-4-20 2 4 6 810 Applied voltage (V)

1 2 strain = d31V/t (d33=275pC/N , d31=-115pC/N ) 1 direct measurement 2 inferred from mechanical motion

Sang-Gook Kim, MIT 43 Using computer microvision system