1. Высшие электромеханические взаимодействия в сегнетоэлектриках
Alexander K. Tagantsev
Ceramics Laboratory
Swiss Federal Institute of Technology (EPFL)
Switzerland
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Applicable Notes

2. Electromechanical coupling in ferroelectrics
Electrostriction !!!
- polarization
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- strain
- stress
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3. Electrostriction in applications
Piezoelectricity in ferroelectric phase
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4. Commercial FBAR ~ SAW /BAW hybrid duplexer Film Bulk Acoustic
ac. wave
piezoelectric
AlN ~
Film Bulk Acoustic
Wave Resonator
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SAW /BAW hybrid duplexer
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5. Electrostriction in applications
Tunable
Film Bulk Acoustic Wave Resonator
(FBAR) ~
(Ba,Sr)TiO3
paraelectric
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6. Electrostriction in applications
Tunable FBAR
admittance
Increasing Edc
670KV/cm
133kV/cm
0kV/cm
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BST device - Noeth et al (2008)
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7. Electrostriction in materials properties
Temperature/misfit-strain film diagrams
Single-domain Landau theory
Phase-field modeling
PbTiO3
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Pertzev et al (1998)
Li et al (2001)
Applicable Notes

8. Electrostriction is the king! Who might threaten the king?
Non-linear
electrostriction
Non-linear
elasticity
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9. g’s in films are fully controlled by “enemies”
Where is the danger?
Film diagrams
Tunable FBARs
antiresonance
g’s in films are fully controlled by “enemies”
Antiresonce frequency
is essentially
controlled by “enemies”
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Applicable Notes

10. Non-linear
elasticity
Non-linear
electrostriction

11. High-order electro-mechanics and thermodynamics of this films
Kvasov and Tagantsev (2012)

12. Thermodynamic potential of film (simple model)
Bulk
“Film”: e = ep

13. Thermodynamic potential of film (simple model)
a  a*: shift of Tc
“Film”: e = ep
SrTiO3
Haeni et al (2004)

14. Thermodynamic potential of film (simple model)
b < 0  b* > 0: change of transition order
“Film”: e = ep

15. Thermodynamic potential of film (simple model)
“Film”: e = ep
What is wrong with g ?

16. Thermodynamic potential of film (simple model)
Bulk
“Film”: e = ep

17. Can one confirm atomic estimates with ab initio calculation?
Expected to be a strong correction
Can one confirm atomic estimates
with ab initio calculation?
What is the impact of the renormalization
in a real material?
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18. First principles calculations
BaTiO3
Helmholtz F(P, ε)
Gibbs G(P, σ)
Equation
of state
Legendre
transformation

19. First principles calculations
Density Functional Theory (DFT)
full relaxation calculations
BaTiO3
Vienna Ab-initio Simulation Package (VASP)
with projector augmented-wave method
6x6x6 Monkhorst-Pack grid
Energy cut-off = 600eV
Hellman-Feynman force < 1meV/A.

20. Calculations: elasticity
σ(ε) dependence, keeping mmm symmetry, P = 0 σ
VASP ε

21. Calculations: electrostriction
P(ε) and s(ε) keeping 4mm tetragonal symmetry ε
P(ε) σ
VASP

22. Renormalization of G-potential for (001) film
Bulk BaTiO3
free film
film on substrate
Paraelectric phase

23. Renormalization of G-potential for (001) film

24. Renormalization of P6- terms for (001) BaTiO3 film

25. Modification of T-em diagram for for (001) BaTiO3 film
Experimental A
Ab initio
Experimental
Ab initio B

26. T-em diagram for for (001) BaTiO3 film
Experimental A
Ab initio
T, K
T, K
Pertzev et al (1998)
em,%
em,%
Applicable Notes

27. T-em diagram for for (001) BaTiO3 film
Experimental B
Ab initio
T, K
T, K
em,%
em,%
Applicable Notes

28. Message Once P6-terms are important for thermodynamics of a ferroelectric, high-order electro-mechanics is important for correct description of this films (single-domain, phase-field etc.)

29. High-order electro-mechanics and tunable FBARs
Noeth et al (2008)

30. Tunable FBAR G S Al BST membrane Pt Noeth et al (2008)
SiO2(100nm)
BST(300nm)
Al(300nm)
Pt(100nm)
ground
signal
non-piezoelectric
BST Al Pt
membrane G S
Outline the high points of the presentation you are giving. Don’t include the title or conclusions in your Outline Slide. You may want to state the purpose of the work described in your paper. If so, describe the big picture of why you did the work, not the detailed technical objectives your work accomplished.
Noeth et al (2008)

31. Resonance and anti-resonance
admittance
current
voltage
resonance
antiresonance

32. Resonance and anti-resonance
tuning
resonance
antiresonance

33. Physics of tuning Field-induced piezoelectricity Resonance
Antiresonance
background permittivity

34. Physics of tuning
resonance
antiresonance
comparable

35. Effect of non-linear electrostriction on FBAR tuning
Antiresonance tuning is essentially controlled by “m”
m < 0
m = 0
m > 0

36. Conclusion Both in physics and applications
it may be dangerous to forget about
high-order electromechanical effects
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37. Andy Noeth Alexander Kvasov
Your first slide must be the Title Slide. The suggested format is shown above. (You may adapt this slide to suit your tastes.) It is recommended that your company or university logo appear on the title slide only. This is followed by your Outline Slide and the other slides mentioned in this template.
For additional details, please see the excellent article on giving a good presentation with quality slides. It is posted on the IMS2004 web site:
Joseph F. White, “Your Paper Has Been Accepted!”, Applied Microwave & Wireless, Winter 1996, pp
Andy Noeth
Alexander Kvasov

38. Thank you!
High visual contrast is very important. If your slides are difficult to read, then the audience will concentrate on reading them and not concentrate on what you are saying. Or they may just walk out on you...
We suggest a few tried and proven color schemes that will produce highly visible visual aids and will also reproduce well in black and white, i.e., the printed workshop books.
Every year a few authors ignore warnings about yellow, white, and light green. Each year there are negative yellow card comments about the authors who use these inappropriate color schemes.
Colors that look good on computer monitors do not necessarily project well. The best advice is: Do not use white, yellow, or light green slide lettering under any circumstances ! Other colors, including light blue or other muted tones, are also a common problem.

39. Renormalization of P4- and P6- terms+

40. Renormalization of P4- and P6- terms

41. Calculations: results