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. Z b/2 β β β X - b/2 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 β β β 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 number f (MHz) b/2p (mm-1) ux uy uz Mode type 1 0.08 0.1 0.146 0.001 1 A0 2 0.43 0.1 0.025 1 0.001 SS0 3 0.64 0.1 1 0.02 0.049 S0 4 3.60 0.1 0.023 1 0.003 SA1 5 4.23 0.1 1 0.01 0.101 A1 6 6.92 0.1 1 0.03 0.697 S1 7 7.09 0.1 0.058 1 0.025 SS1 8 7.44 0.1 0.541 0.013 1 S2 Mode identification • The modes are identified by the dominant component of acoustical displacement IEEE UFFC, N12, 2008, accepted.

8. β β β X3 β X3 X3 X3 X1 X1 X1 X1 S0(3) S1(6) S2(8) β X3 X1 A0(1) A1(5) X3 X3 X3 β X2 β X2 X2 X1 X1 X1 SA1(4) SS1(7) SS0(2) Plate acoustic modes

9. Piezoelectric coupling coefficient (K2) 1 – A0, 2 – SS0, 3 – S0, 4 – SA1, 5 – A1, 6 – S1, 7 – SS1, 8 – S2 • K2 = 2(V0-Vm) / V0 (Kempbell, Jones, Ingebrigsten) • V0 - phase velocity with free surfaces • Vm- phase velocity with one surface metallized Note: For surface waves K2~0.03 IEEE UFFC, N12, 2008, accepted.

10. out RF in (A1) (A1) (S2) (S2) 6 (S1) paw 6 (S1) 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. 8 7 6 5 4 3 2 1 λ=D FEM dispersion curves for sample #1 • Plate with free surfaces, N = 150 domains, D = 0.6 mm. D=0.6 mm b 45mm 75mm λ = 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 D=0.6 mm Original crystal X -Y

14. 8 4 5 6 5 4 2 3 λ = D 1 λ=D 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. 5 1 3 λ = D 1 λ=D 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

16. Experimental group velocity • Group velocity of modes A0 and SA1 is zero at stop-bands Vg=dw/dβ (4) (1) (1) (4)

17. 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. Z b/2 β β β X - b/2 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

24. 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