Plate acoustic waves in ferroelectric wafers

1
Plate acoustic waves in ferroelectric wafers

• V. A. Klymko
• Department of Physics and Astronomy
• University of Mississippi

2
Why study plate waves in ferroelectrics?

• Current applications for lithium niobate plates
• Transducers
• Actuators
• Delay lines
• Acousto-optical waveguides
• Optical detectors
• Possible future applications
• Ferroelectric memory for hard drives
• New acoustical and RF filters
• Phononic materials featuring stop bands

3
Outline

• Plate waves in single crystal LiNbO3
• Method of partial waves
• Experiment
• Piezoelectric coupling coefficient
• Plate waves in periodically poled LiNbO3
• Finite Element method
• Numerical results
• Experimental data
• Group velocity dispersion curves
• Conclusions

4
Numerical solution equations

• Equation
• of motion
• Piezoelectric
• relations
• General solution

5
Numerical solution boundary conditions

• Zero normal component of the stress
• Continuous electric displacement

X3
b/2
ß
ß
ß
X1
- b/2
.
6
Dispersion curves single crystal LINbO3

• Numerical solution and experiment

8
8
7
7
5
6
5
4
3
4
3
2
2
1
1
1- A0, 2 SS0, 3 S0, 4- SA1, 5 A1, 6 S1, 7
SS1, 8 S2
Accepted to IEEE Trans. on UFFC
7
Mode identification

• The modes are identified by the dominant
  component of acoustical displacement

IEEE UFFC, N12, 2008, accepted.
8
Plate acoustic modes
9
Piezoelectric coupling coefficient (K2)

• K2 2(V0-Vm) / V0 (Kempbell, Jones,
  Ingebrigsten)
• V0 - phase velocity with free surfaces
• Vm- phase velocity with one surface metallized

1 A0, 2 SS0, 3 S0, 4 SA1, 5 A1, 6
S1, 7 SS1, 8 S2
Note For surface waves K20.03
IEEE UFFC, N12, 2008, accepted.
10
Delay line

• Calculated and measured
• transmission coefficient

IEEE UFFC, N12, 2008, accepted.
11
FEM model for periodically poled LiNbO3

• The functional of the total energy is minimized

air
- kinetic
Absorbing load
Absorbing load
Input transducer

• energy of
• electric field

LiNbO3
- elastic
air
X3
- energy of excitation
i 1..6, n 1..N
X1
12
FEM dispersion curves for sample 1

• Plate with free surfaces, N 150 domains, D
  0.6 mm.

D0.6 mm
b
45mm
75mm
? D
1- A0, 2 SS0, 3 S0, 4- SA1, 5 A1, 6 S1, 7
SS1, 8 S2
13
Periodically poled LiNbO3 (sample 1)

• Periodic domains in polarized light

Domain with inverted piezoelectric field
D0.6 mm
Original crystal
X
-Y
14
Experiment sample 1

• Plate with free surfaces, N 150 domains, D
  0.6 mm.

0.6 mm
b
45mm
75mm
1- A0, 2 SS0, 3 S0, 4- SA1, 5 A1, 6 S1, 7
SS1, 8 S2
15
Experiment sample 2

• Plate with free surfaces, N 84 domains, D
  0.9 mm.

0.9 mm
b
40mm
50mm
1- A0, 2 SS0, 3 S0, 4- SA1, 5 A1, 6 S1, 7
SS1, 8 S2
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Experimental group velocity

• Group velocity of modes A0 and SA1 is zero at
  stop-bands

Vgdw/dß
(4)
(1)
(1)
(4)
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Conclusions

• Dispersion curves are computed for PAW in ZX-cut
  LiNbO3.The modes can be identified by their
  dominant components near cutoff frequencies.
• In ZX-cut LiNbO3, modes A1 and S2 have high
  piezoelectric coupling 23 (A1) and 13 (S2),
  which is promising for applications in
  telecommunication.
• Dispersion curves in periodically poled LiNbO3
  (PPLN) are computed and experimentally verified
  for the first time.
• Stop-bands are revealed for the first time in the
  dispersion curves of plate waves propagating in
  PPLN. The group velocity of plate waves decreases
  to zero at stop-band.
• The developed FEM model can be applied for design
  of ultrasonic transducers and delay lines.

18
Acknowledgements

• I would like to thank our faculty, staff, and
  students for their interest in my work
• I am grateful to Drs. Lucien Cremaldi, Mack
  Breazeale, Josh Gladden, James Chambers for many
  useful comments and suggestions
• I would like to thank my advisor Dr. Igor
  Ostrovskii for interesting research topic and
  guidance.
• I appreciate the help of my colleague Dr. Andrew
  Nadtochiy with development of FEM codes.
• The support of the Department of Physics and
  Astronomy and the Graduate School was essential
  for the completion of this work

19
Numerical solution method of partial waves

• Equation of motion
• and equations of state
• with the general solution
• yield Christoffel equation

20
Method of partial waves (2)

• Determinant of the Christoffel equation is solved
  for the propagation constants of partial waves
• General solution is the sum of partial waves

21
Numerical solution boundary conditions

• Stress-free surfaces in the air
• Stress-free surfaces, plate is on a metal
  substrate

.
22
Numerical dispersion curves

• The dispersion curves for three boundary
  conditions

Asymmetric 1 A0 5 A1 Symmetric 3 S0 6
S1 8 - S2 Shear 2 SS0 4 SA1 7 SS1
8
7
6
5
4
3
2
1
23
Experimental setup

• Electric potential is measured using metal
  electrode

• Electric potential is measured using metal
  electrode

Amplifier
Stage
Shield
LiNbO3
Output transducer
X
Input transducer
Metal substrate
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Fabrication of a sample with periodic domains
(Poling)

• 22 kV/mm electric field is applied to the wafer
  surface

Microscope
Electrode (11 kV)
Needle
LiNbO3
Greese
Grounded electrode
Plastic basin with water
Polarizer
Moving stage