Thesis0520

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Thesis0520

  1. 1. A Finite Element Study of Piezoelectric Thin Films on Substrates <ul><li>Bo Liu </li></ul><ul><li>Advisor: Dr. Abhijit Bhattacharyya </li></ul>
  2. 2. OUTLINE OF PRESENTATION <ul><li>Background </li></ul><ul><li>Modeling preliminaries </li></ul><ul><li>Tasks </li></ul><ul><li>List of publications </li></ul>
  3. 3. BACKGROUND <ul><li>Piezoelectricity </li></ul><ul><li>Direct piezoelectric effect </li></ul><ul><ul><li>Electric polarization is </li></ul></ul><ul><ul><li>induced by mechanical </li></ul></ul><ul><ul><li>strain in piezoelectric </li></ul></ul><ul><ul><li>crystals. </li></ul></ul><ul><ul><li>The polarization is </li></ul></ul><ul><ul><li>proportional to the strain. </li></ul></ul><ul><li>Converse piezoelectric effect </li></ul><ul><ul><li>A piezoelectric crystal is </li></ul></ul><ul><ul><li>subjected to an electric field, </li></ul></ul><ul><ul><li>resulting in mechanical strain. </li></ul></ul><ul><ul><li>The strain is proportional to </li></ul></ul><ul><ul><li>the electric field. </li></ul></ul><ul><li>Figures referred from presentation of Chunxiang Zhu, Dept of ECE, National university of Singapore. </li></ul>
  4. 4. BACKGROUND <ul><li>Mechanism of piezoelectricity </li></ul><ul><li>Centrosymmetric crystal </li></ul><ul><li>Non-centrosymmetric crystal </li></ul><ul><li>Figures referred from presentation of Chunxiang Zhu, Dept of ECE, National university of Singapore </li></ul>
  5. 5. BACKGROUND <ul><li>Why piezoelectric thin films on substrates? </li></ul><ul><li>The films are necessary to be very thin, because </li></ul><ul><ul><li>A low voltage can be applied to generate a high electric field. </li></ul></ul><ul><ul><li>Vibration wouldn’t damp because of thickness of the films. </li></ul></ul><ul><li>Piezoelectric thin films on substrates have been used in </li></ul><ul><ul><li>Piezoelectric thin film resonator and filter 1 , </li></ul></ul><ul><ul><li>Piezoelectric thin film vibrator 2 , </li></ul></ul><ul><ul><li>Piezoelectric thin film sensor 3 and actuator 4 . </li></ul></ul><ul><li>S. Taniguchi, T. Yokoyama, M. Hara, T. Sakashita, U.S. Pat. Appl. Publ. A1 , 2007096597 (2007). </li></ul><ul><li>Y. Yamada, T. Yoshida, M. Hashimoto, N. Suzuki, T. Makino, U.S. Pat. Appl. Publ. A1 2003020365 (2003). </li></ul><ul><li>Z. Song, W. Liu, Z. Yan, T. Zhang, J. Cheng, S. Feng, L. Lai, and J. Chen, Pat. Appl. Country: CN, 1004-418, 18. 2007 </li></ul><ul><li>J. Park, R.K. Nakahira, R.C. Allison, U.S. Pat. Appl. Publ. A1 2004094815 (2004). </li></ul>
  6. 6. BACKGROUND <ul><li>Applications </li></ul><ul><li>High density digital memories 1 </li></ul><ul><ul><li>High density, </li></ul></ul><ul><ul><li>Very fast operating speed (30 nanoseconds), </li></ul></ul><ul><ul><li>Low operating voltage, </li></ul></ul><ul><ul><li>Nonvolatility(non-retention), </li></ul></ul><ul><ul><li>Extreme radiation hardness. </li></ul></ul><ul><li>Surface acoustic wave (SAW) devices 2 </li></ul><ul><ul><li>SAW filters, </li></ul></ul><ul><ul><li>SAW sensors. </li></ul></ul><ul><li>Ultrasound transducers </li></ul><ul><ul><li>High-quality imaging probes. </li></ul></ul><ul><li>1. James F. Scott, Carlos A Paz De Araujo, Science, Vol.246 1400-1405 2007 </li></ul><ul><li>2. M. Hofer, N. Finger, G. Kovacs,. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. Vol.53. No6. 1192-1201 2006 </li></ul><ul><li>3. S. Ballandras, M. Wilm, PF. Edoa, A. Soufyane, V. Laude,. Journal of Applied Physics. Vol.93. No1.702-711 2003 </li></ul>
  7. 7. BACKGROUND <ul><li>Literature Survey </li></ul><ul><li>Deposition of thin piezoelectric films on substrates resulting in an effective film response weaker than the response of a free standing film. This outcome is due to following reasons: </li></ul><ul><ul><li>Substrate bending 1 , </li></ul></ul><ul><ul><li>Clamping effects of the substrate on the film 2 , </li></ul></ul><ul><ul><li>Lattice mismatch 3 , </li></ul></ul><ul><ul><li>Dislocation generation 4 , </li></ul></ul><ul><ul><li>Geometric dimensions of the film and the substrate 2,5 , </li></ul></ul><ul><ul><li>The stiffness of the film and the substrate 1 . </li></ul></ul><ul><li>J. -. Li, L. Chen, V. Nagarajan, R. Ramesh, and A. L. Roytburd, Appl. Phys. Lett. 84 , 2626 (2004). </li></ul><ul><li>K. Lee, H. Yi, W. Park, Y. K. Kim, and S. Baik, J. Appl. Phys. 100 , 051615/1 (2006). </li></ul><ul><li>G. Catalan, B. Noheda, J. McAneney, L. J. Sinnamon, and J. M. Gregg, Physical Review B: Condensed Matter and Materials Physics 72 , 020102/1 (2005). </li></ul><ul><li>S. P. Alpay, I. B. Misirlioglu, V. Nagarajan, and R. Ramesh, Appl. Phys. Lett. 85 , 2044 (2004). </li></ul><ul><li>C. Lichtensteiger, J. Triscone, J. Junquera, and P. Ghosez, Phys. Rev. Lett. 94 , 047603/1 (2005). </li></ul>Effect of island periodicity has not been studied
  8. 8. BACKGROUND <ul><li>Motivation </li></ul><ul><li>Piezoresponse of periodic thin film islands on substrates </li></ul><ul><ul><li>different shape of islands, </li></ul></ul><ul><ul><li>X-periodicity and XY-periodicity, </li></ul></ul><ul><ul><li>geometric dimensional effects, </li></ul></ul><ul><ul><li>relative stiffness effects. </li></ul></ul><ul><li>Internal stress states of periodic thin film islands on substrates </li></ul><ul><ul><li>internal stress could result in dislocation generation and fracture, </li></ul></ul><ul><ul><li>If thin film also have ferroelectric properties, internal stress could stimulate </li></ul></ul><ul><ul><li>phase transformation. </li></ul></ul>
  9. 9. BACKGROUND <ul><li>Main Contribution </li></ul><ul><li>To advance the understanding of the degradation in the response of piezoelectric thin films after deposition we studied </li></ul><ul><ul><li>The “effective” piezoelectric coefficients of converse response of BT/MgO, PZT/STO and ZnO/STO, </li></ul></ul><ul><ul><li>The clamping effects of the substrate, lattice mismatch, different stiffness of the films and the substrates. </li></ul></ul><ul><li>Periodic structure is a pattern to overcome the degradation of piezoresponse </li></ul><ul><li>Bi-island structure has more advantages </li></ul><ul><ul><li>Additional contribution to improve the piezoresponse, </li></ul></ul><ul><ul><li>Hybrid device. </li></ul></ul>
  10. 10. Description of the periodic structure MODELING PRELIMINARIES
  11. 11. MODELING PRELIMINARIES <ul><li>Governing equations </li></ul><ul><li>The electromechanical constitutive equations 1 </li></ul><ul><li>Equilibrium equations 1 </li></ul><ul><li>W.G. Cady, Piezoelectricity; Dover Publications, New York, 1964 </li></ul>
  12. 12. MODELING PRELIMINARIES <ul><li>Non-dimensionalization </li></ul><ul><li>Introduce following non-dimensional parameters </li></ul><ul><li>Non-dimensionalized constitutive equations </li></ul><ul><ul><li>constitutive equations </li></ul></ul><ul><ul><li>Equilibrium equations </li></ul></ul><ul><li>Following non-dimensional parameters have been identified </li></ul>
  13. 13. MODELING PRELIMINARIES 1. Z. Bo, &quot;Constitutive Modeling of Shape Memory Alloys&quot;, Doctoral Dissertation, Texas A&M University. (1996). Mechanical boundary conditions
  14. 14. MODELING PRELIMINARIES Electrical boundary conditions
  15. 15. MODELING PRELIMINARIES <ul><li>Other conditions </li></ul><ul><li>Computations with the free boundary conditions are </li></ul><ul><li>modeled by replacing conditions (ii) and (iv) above </li></ul><ul><li>with a traction free condition, . </li></ul><ul><li>The converse piezoelectric effect is modeled by setting </li></ul><ul><li>in (viii) and in (x). </li></ul><ul><li>The direct piezoelectric effect is modeled by setting in (x) and </li></ul><ul><li>in (viii). </li></ul>
  16. 16. MODELING PRELIMINARIES <ul><li>To consider the lattice mismatch the constitutive equations become: </li></ul><ul><li>To estimate the “overall” internal stresses, a scalar internal stress parameter, </li></ul><ul><li>, and its volume average, , are defined as </li></ul><ul><li>is the volume of the thin film. </li></ul><ul><li>Effective piezoelectric coefficient </li></ul><ul><li>Free standing film Film on substrate </li></ul><ul><li>……… converse effect ………converse effect 1 </li></ul><ul><li>……… direct effect ………direct effect </li></ul><ul><li>J. -. Li, L. Chen, V. Nagarajan, R. Ramesh, and A. L. Roytburd, Appl. Phys. Lett. 84 , 2626 (2004). </li></ul>
  17. 17. MODELING PRELIMINARIES <ul><li>Analysis parameters </li></ul><ul><li>The effect of the normalized radius of the thin film islands ( ). </li></ul><ul><li>Normalized inter-island spacing ( ). </li></ul><ul><li>The ratio of the stiffness ( ) due to biaxial loading on film to that of the substrate and the stiffness ratio ( ) between the inserted island and the substrate. </li></ul><ul><li>where Y s and are the Young’s modulus and Poisson’s ratio of substrate respectively. The subscript i indicate the inserted non-piezoelectric island. </li></ul><ul><li>The penetration depth of the strain . </li></ul>
  18. 18. MODELING PRELIMINARIES <ul><li>Material properties of BT 1 , PZT 2 , ZnO 3 thin films and MgO 4 , STO 5 substrate </li></ul><ul><li>S. N. Hari, Handbook of Thin Film Materials 5 Volume set, Academic Press (2001). </li></ul><ul><li>http://www.efunda.com/materials/piezo/material_data/matdata_output.cfm?Material ID=PZT-5A . </li></ul><ul><li>G. Carlotti, G. Socino, A. Petri, and E. Verona, Ultrasonics Symposium Proceedings, 295 (1987). </li></ul><ul><li>J. Zhang, L. Zhang, X. Peng, X. Wang, Appl. Phys. A 73 , 773-775 (2001). </li></ul><ul><li>H. Ledbetter, M. Lei, and S. Kim, Phase Transitions 23 , 61 (1990). </li></ul>0.232 0.166 Poisson’s ratio 189.7 310.5 Young’s modulus Y (GPa) STO MgO
  19. 19. MODELING PRELIMINARIES <ul><li>Finite element mesh </li></ul><ul><li>3D solid elements (type: C3D6E) with optimized grid seeds </li></ul><ul><li>The mesh uniform on the xy plane and non-uniform along the z-direction. </li></ul><ul><li>Non-uniformity is defined by , An identical non-uniformity in mesh generation is implemented in the substrate from the interface to a depth equal to the thickness of the film. </li></ul>
  20. 20. TASKS <ul><li>The research reported in this dissertation includes following sections </li></ul><ul><ul><li>A computational study of the response of periodic piezoelectric thin films on substrates (Section 4), </li></ul></ul><ul><ul><li>A computational analysis of the interactions of geometric periodicity and lattice mismatch on the electromechanical response of piezoelectric thin films (Section 5), </li></ul></ul><ul><ul><li>A comparative numerical study of piezoelectric materials with tetragonal and hexagonal transversely isotropic symmetry on isotropic substrates (Section 6), </li></ul></ul><ul><ul><li>Piezoelectric response and internal stress of periodic bi-island piezoelectric thin films on substrates (Section 7). </li></ul></ul>
  21. 21. A computational analysis of the interactions of geometric periodicity and lattice mismatch on the electromechanical response of piezoelectric thin films <ul><li>Lattice mismatch </li></ul><ul><li>Internal strain caused by lattice mismatch </li></ul><ul><li>and are the in-plane lattice parameters of the thin film and </li></ul><ul><li>the substrate respectively. </li></ul><ul><li>Strain gradient theory (SG) 1 </li></ul><ul><li>“ z” is the vertical coordinate. </li></ul><ul><li>is the penetration depth of the strain </li></ul><ul><li>Approximate strain-gradient theory (ASG) when </li></ul><ul><li>The equivalent position dependent thermal coefficient </li></ul><ul><li>is the spatially uniform </li></ul><ul><li>temperature excursion of </li></ul><ul><li>the thin film. </li></ul><ul><li>G. Catalan, B. Noheda, J. McAneney, L. J. Sinnamon, and J. M. Gregg, Physical Review B: Condensed Matter and Materials Physics 72 , 020102/1 (2005). </li></ul>
  22. 22. TASK B <ul><li>Plot of S.G and A.S.G for two different penetration depth </li></ul>
  23. 23. TASK B Optimization of the mesh
  24. 24. TASK B Internal stress
  25. 25. TASK B Normalized displacement
  26. 26. A comparative numerical study of piezoelectric materials with tetragonal and hexagonal transversely isotropic symmetry on isotropic substrates <ul><li>Optimized grid seeds for BT/MgO, PZT/STO and ZnO/ STO. </li></ul>
  27. 27. TASK C <ul><li>Influence of different components of piezoelectric coefficient on the “effective” coefficient </li></ul><ul><li>Transversely isotropic piezoelectric compliance tensor </li></ul><ul><li>Boundary condition </li></ul>
  28. 28. TASK C Other effects on “effective” piezoelectric coefficient
  29. 29. Piezoelectric response and internal stress of periodic bi-island piezoelectric thin films on substrates <ul><li>Relative normalized displacement </li></ul>
  30. 30. TASK D Stiffness ratio effect
  31. 31. TASK D Internal stress
  32. 32. TASK D Effects of different stiffness on internal stress
  33. 33. Ferroelectricity <ul><li>Barium Titanate crystal at </li></ul><ul><li>a bove Curie Temperature (T c ) </li></ul><ul><li>Barium Titanate crystal at </li></ul><ul><li>b elow Curie Temperature </li></ul><ul><li>Figures referred from presentation of Chunxiang Zhu, Dept of ECE, National university of Singapore </li></ul>
  34. 34. LIST OF PUBLICATIONS <ul><li>Journal papers </li></ul><ul><li>Liu, B., Pidugu, S., Bhattacharyya, A., 2008, A computational study of the response of periodic piezoelectric thin films on substrates, Physical Review B , 77, 024102 </li></ul><ul><li>Liu, B., Pidugu, S., Bhattacharyya, A., 2008, A comparative numerical study of piezoelectric materials with tetragonal and hexagonal transversely isotropic symmetry on isotropic substrates (submitted). </li></ul><ul><li>Liu, B., Pidugu, S., Bhattacharyya, A., 2008, A computational analysis of the interactions of geometric periodicity and lattice mismatch on the electromechanical response of piezoelectric thin films (in propose). </li></ul><ul><li>Liu, B., Pidugu, S., Bhattacharyya, A., 2008, Piezoelectric response and internal stress of periodic bi-island piezoelectric thin films on substrate (in propose). </li></ul><ul><li>Conference papers </li></ul><ul><li>Liu, B., Bhattacharyya, A., 2007, “Effect of substrate and lattice mismatch on the response of piezoelectric thin films”, Proceedings of the Symposium J: Materials for Advanced Sensors and Detectors, International Conference on Materials for Advanced Technologies, July 1-6, 2007, Singapore (12 pages). </li></ul><ul><li>Liu, B., Bhattacharyya, A., 2007, “The interactions of geometric periodicity and lattice mismatch on the electromechanical response of piezoelectric thin films”, 40th International Symposium on Microelectronics, Nov 11-15, 2007 (7 pages). </li></ul><ul><li>Liu, B., Bhattacharyya, A., 2006, The Effect of Lattice Mismatch on the Piezoresponse of Barium Titanate (BaTiO3) Thin Films on Magnesium Oxide (MgO) Substrates, 39th International Symposium on Microelectronics, Oct 8-12, 2006 (6 pages). </li></ul><ul><li>Liu, B., Bourdo, S., Dervishi, E., Berry, B., Kim, H., Bhattacharyya, A., Viswanathan, T., 2004, “Graphite-polymer coatings for electrically induced thermal actuation of shape memory alloys”, Smart Structures and Materials 2004: Industrial and Commercial Applications of Smart Structures Technologies (Ed.: Eric H. Anderson), SPIE Vol.5388, 355-363. </li></ul>
  35. 35. <ul><li>Questions ? </li></ul><ul><li>Comments ? </li></ul><ul><li>Thank you </li></ul>

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