Monte Carlo Simulation of Ferroelectric Behavior in PZT Films by Using a Stress Dependent DIFFOUR Hamiltonian
Main Article Content
Keywords
Monte Carlo, simulation, ferroelectrics, DIFFOUR, PZT.
Abstract
In this work the polarization and hysteresis response of Lead Zirconate Titanate (PZT) ferroelectric thin films was studied in relation to the variation on temperature, stress, electric field and the content of non-ferroelectric impurities by using a Monte Carlo simulation. The simulation was based on a DIFFOUR Hamiltonian that takes into account the effect of uniaxial stress, in addition to the nearest neighbor dipoles interaction and the effect of an external electric field. The obtained results for hysteresis loops and polarization curves correspond with reported experimental data for this material.
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References
[1] S. Watanabe, T. Fujiu, and T. Fujii, “Effect of poling on piezoelectric properties of lead zirconate titanate thin films formed by sputtering,” Applied Physics Letters, vol. 66, no. 12, pp. 148–150, 1995.
[2] P. Luginbuhl, G.-A. Racine, P. Lerch, B. Romanowicz, K. G. Brooks, N. F. de Rooij, P. Renaud, and N. Setter, “Piezoelectric cantilever beams actuated by {PZT} sol-gel thin film,” Sensors and Actuators A: Physical, vol. 54, no. 1–3, pp. 530–535, 1996.
[3] Y. Miyahara, M. Deschler, T. Fujii, S. Watanabe, and H. Bleuler, “Noncontact atomic force microscope with a {PZT} cantilever used for deflection sensing, direct oscillation and feedback actuation,” Applied Surface Science,
vol. 188, no. 3-4, pp. 450–455, 2002.
[4] P. Muralt, M. Kohli, T. Maeder, A. Kholkin, K. Brooks, N. Setter, and R. Luthier, “Fabrication and characterization of {PZT} thin-film vibrators for micromotors,” Sensors and Actuators A: Physical, vol. 48, no. 2, pp. 157–165, 1995.
[5] M. Dubois and P. Muralt, “PZT thin film actuated elastic fin micromotor,” Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, vol. 45, no. 5, pp. 1169–1177, 1998.
[6] A. M. Flynn, L. S. Tavrow, S. F. Bart, R. A. Brooks, D. Ehrlich, K. R. Udayakumar, and L. E. Cross, “Piezoelectric micromotors for microrobots,” Microelectromechanical Systems, Journal of, vol. 1, no. 1, pp. 44–51, Mar. 1992. [Online]. Available: http://dx.doi.org/10.1109/84.128055
[7] P. Luginbuhl, S. D. Collins, G.-A. Racine, M.-A. Gretillat, N.-F. de Rooij, K. G. Brooks, and N. Setter, “Microfabricated Lamb wave device based on PZT sol-gel thin film for mechanical transport of solid particles and liquids,” Microelectromechanical Systems, Journal of, vol. 6, no. 4, pp. 337–346, 1997.
[8] P. Muralt, “Ferroelectric thin films for micro-sensors and actuators: a review,” Journal of Micromechanics and Microengineering, vol. 10, no. 2, pp. 136–146, 2000.
[9] G. Haertling, Piezoelectric and electrooptic ceramics, 1st ed., ser. Materials engineering, R. Buchanan Dekker, Ed. New York: Taylor & Francis, 1986.
[10] M. Rios Gutierrez and G. Silva, “Control de vibraciones en estructuras tipo edificio usando actuadores piezoeléctricos y retroalimentación positiva de la aceleración,” DYNA, vol. 80, no. 179, pp. 116–125, Jun. 2013. [Online].
Available: http://dx.doi.org/10.15446/dyna.v80n179.30733
[11] M. Strikha, “Non-volatile memory and IR radiation modulators based upon graphene-on-ferroelectric substrate. A review,” Ukrainian Journal of Physical Optics, vol. 13, no. 3, pp. s15–s12, 1995.
[12] D. Landínez Tellez, G. Peña Rodríguez, F. Fajardo, J. Rodríguez, and J. Roa Rojas, “Structural, magnetic, multiferroic, and electronic properties of Sr2TiMnO6 double perovskite,” DYNA, vol. 79, no. 171, pp. 111–115, 2012. [Online]. Available: http://dx.doi.org/10.15446/dyna.v79n171.18104
[13] C. Bedoya Hincapié, M. Pinzón Cárdenas, J. Alfonso Orjuela, and E. Restrepo Parra, “Propiedades fisicoquímicas del bimuto y óxidos de bismuto: síntesis, caracterización y aplicaciones,” DYNA, vol. 79, no. 176, pp. 139–148, 2012.
[14] N. Wongdamnern, N. Triamnak, A. Ngamjarurojana, Y. Laosiritaworn, S. Ananta, and R. Yimnirun, “Comparative studies of dynamic hysteresis responses in hard and soft {PZT} ceramics,” Ceramics International, vol. 34, no. 4, pp. 731–734, 2008.
[15] Y. Laosiritaworn, S. Ananta, J. Poulter, and R. Yimnirun, “Monte Carlo investigation of hysteresis properties in ferroelectric thin-films under the effect of uniaxial stresses,” Ceramics International, vol. 35, no. 1, pp. 181–184, 2009.
[16] B. Jaffe, W. R. Cook, and H. L. Jaffe, Piezoelectric ceramics, ser. Nonmetallic solids. Academic Press, 1971.
[17] Y. J. Song, Y. Zhu, and S. B. Desu, “Low temperature fabrication and properties of sol-gel derived (111) oriented Pb(Zr1-xTix)O3 thin films,” Applied Physics Letters, vol. 72, no. 21, pp. 2686–2688, 1998. [Online]. Available: http://dx.doi.org/10.1063/1.121099
[18] N. Tohge, S. Takahashi, and T. Minami, “Preparation of PbZrO3-PbTiO3 Ferroelectric Thin Films by the Sol-Gel Process,” Journal of the American Ceramic Society, vol. 74, no. 1, pp. 67–71, 1991.
[19] S. r. F. Jarner and E. Hansen, “Geometric ergodicity of Metropolis algorithms,” Stochastic Processes and their Applications,
vol. 85, no. 2, pp. 341–361, 2000. [Online]. Available: http://dx.doi.org/10.1016/S0304-4149(99)00082-4
[20] T. Janssen and J. A. Tjon, “One-dimensional model for a crystal with displacive modulation,” Phys. Rev. B, vol. 24, no. 4, pp. 2245–2248, 1981. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.24.2245
[21] J.-M. Liu, W. M. Wang, Z. G. Liu, H. L. Chan, and C. L. Choy, “Dynamic hysteresis in ferroelectric systems: experiment and Monte Carlo simulation,” Applied Physics A, vol. 75, no. 4, pp. 507–514, 2002. [Online]. Available:
http://dx.doi.org/10.1007/s003390101012
[22] Y.-Z. Wu, D.-L. Yao, and Z.-Y. Li, “Monte-Carlo simulation of the switching behavior in ferroelectrics with dipolar defects,” Solid State Communications, vol. 122, no. 7-8, pp. 395–400, 2002.
[23] J. Hong and D. Fang, “Systematic study of the ferroelectric properties of Pb(Zr0.5Ti0.5)O3 nanowires,” Journal of Applied Physics, vol. 104, no. 6, pp. –, 2008. [Online]. Available: http://dx.doi.org/10.1063/1.2982090
[24] R. Yimnirun, Y. Laosiritaworn, and S. Wongsaenmai, “Effect of uniaxial compressive pre-stress on ferroelectric properties of soft PZT ceramics,” Journal of Physics D: Applied Physics, vol. 39, no. 4, p. 759, 2006. [Online]. Available: http://stacks.iop.org/0022-3727/39/i=4/a=025
[25] W. Smiga and B. Garbarz-Glos, “Studies of the influence of uniaxial pressure on the electric behaviour of Li0.015Na0.985NbO3 ceramics,” Ukrainian Journal of Physical Optics, vol. 13, no. 4, p. S27, 2012. [Online]. Available:
http://dx.doi.org/10.3116/16091833/13/1/s27/2012
[26] M. D. Nguyen, M. Dekkers, E. Houwman, R. Steenwelle, X. Wan, A. Roelofs, T. Schmitz-Kempen, and G. Rijnders, “Misfit strain dependence of ferroelectric and piezoelectric properties of clamped (001) epitaxial Pb(Zr0.52,Ti0.48)O3 thin films,” Applied Physics Letters, vol. 99, no. 25, pp. –, 2011. [Online]. Available: http://dx.doi.org/10.1063/1.3669527
[27] J. Suchanicz, N. T. H. Kim-Ngan, K. Konieczny, I. Jankowska-Sumara, D. Sitko, D. Goc-Jaglo, and A. G. Balogh, “Influence of combined external stress and electric field on electric properties of 0.5% Fe-doped lead zirconate titanate ceramics,” Journal of Applied Physics, vol. 106, no. 9, pp. 94 104–94 109, 2009. [Online]. Available: http://dx.doi.org/10.1063/1.3234394
[28] D. Guo, K. Cai, L. Li, and Z. Gui, “Investigation of the additive induced doping effects in gelcast soft lead zirconate titanate ceramics,” Journal of Applied Physics, vol. 106, no. 5, p. 054104, 2009. [Online]. Available: http://dx.doi.org/10.1063/1.3190549
[2] P. Luginbuhl, G.-A. Racine, P. Lerch, B. Romanowicz, K. G. Brooks, N. F. de Rooij, P. Renaud, and N. Setter, “Piezoelectric cantilever beams actuated by {PZT} sol-gel thin film,” Sensors and Actuators A: Physical, vol. 54, no. 1–3, pp. 530–535, 1996.
[3] Y. Miyahara, M. Deschler, T. Fujii, S. Watanabe, and H. Bleuler, “Noncontact atomic force microscope with a {PZT} cantilever used for deflection sensing, direct oscillation and feedback actuation,” Applied Surface Science,
vol. 188, no. 3-4, pp. 450–455, 2002.
[4] P. Muralt, M. Kohli, T. Maeder, A. Kholkin, K. Brooks, N. Setter, and R. Luthier, “Fabrication and characterization of {PZT} thin-film vibrators for micromotors,” Sensors and Actuators A: Physical, vol. 48, no. 2, pp. 157–165, 1995.
[5] M. Dubois and P. Muralt, “PZT thin film actuated elastic fin micromotor,” Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, vol. 45, no. 5, pp. 1169–1177, 1998.
[6] A. M. Flynn, L. S. Tavrow, S. F. Bart, R. A. Brooks, D. Ehrlich, K. R. Udayakumar, and L. E. Cross, “Piezoelectric micromotors for microrobots,” Microelectromechanical Systems, Journal of, vol. 1, no. 1, pp. 44–51, Mar. 1992. [Online]. Available: http://dx.doi.org/10.1109/84.128055
[7] P. Luginbuhl, S. D. Collins, G.-A. Racine, M.-A. Gretillat, N.-F. de Rooij, K. G. Brooks, and N. Setter, “Microfabricated Lamb wave device based on PZT sol-gel thin film for mechanical transport of solid particles and liquids,” Microelectromechanical Systems, Journal of, vol. 6, no. 4, pp. 337–346, 1997.
[8] P. Muralt, “Ferroelectric thin films for micro-sensors and actuators: a review,” Journal of Micromechanics and Microengineering, vol. 10, no. 2, pp. 136–146, 2000.
[9] G. Haertling, Piezoelectric and electrooptic ceramics, 1st ed., ser. Materials engineering, R. Buchanan Dekker, Ed. New York: Taylor & Francis, 1986.
[10] M. Rios Gutierrez and G. Silva, “Control de vibraciones en estructuras tipo edificio usando actuadores piezoeléctricos y retroalimentación positiva de la aceleración,” DYNA, vol. 80, no. 179, pp. 116–125, Jun. 2013. [Online].
Available: http://dx.doi.org/10.15446/dyna.v80n179.30733
[11] M. Strikha, “Non-volatile memory and IR radiation modulators based upon graphene-on-ferroelectric substrate. A review,” Ukrainian Journal of Physical Optics, vol. 13, no. 3, pp. s15–s12, 1995.
[12] D. Landínez Tellez, G. Peña Rodríguez, F. Fajardo, J. Rodríguez, and J. Roa Rojas, “Structural, magnetic, multiferroic, and electronic properties of Sr2TiMnO6 double perovskite,” DYNA, vol. 79, no. 171, pp. 111–115, 2012. [Online]. Available: http://dx.doi.org/10.15446/dyna.v79n171.18104
[13] C. Bedoya Hincapié, M. Pinzón Cárdenas, J. Alfonso Orjuela, and E. Restrepo Parra, “Propiedades fisicoquímicas del bimuto y óxidos de bismuto: síntesis, caracterización y aplicaciones,” DYNA, vol. 79, no. 176, pp. 139–148, 2012.
[14] N. Wongdamnern, N. Triamnak, A. Ngamjarurojana, Y. Laosiritaworn, S. Ananta, and R. Yimnirun, “Comparative studies of dynamic hysteresis responses in hard and soft {PZT} ceramics,” Ceramics International, vol. 34, no. 4, pp. 731–734, 2008.
[15] Y. Laosiritaworn, S. Ananta, J. Poulter, and R. Yimnirun, “Monte Carlo investigation of hysteresis properties in ferroelectric thin-films under the effect of uniaxial stresses,” Ceramics International, vol. 35, no. 1, pp. 181–184, 2009.
[16] B. Jaffe, W. R. Cook, and H. L. Jaffe, Piezoelectric ceramics, ser. Nonmetallic solids. Academic Press, 1971.
[17] Y. J. Song, Y. Zhu, and S. B. Desu, “Low temperature fabrication and properties of sol-gel derived (111) oriented Pb(Zr1-xTix)O3 thin films,” Applied Physics Letters, vol. 72, no. 21, pp. 2686–2688, 1998. [Online]. Available: http://dx.doi.org/10.1063/1.121099
[18] N. Tohge, S. Takahashi, and T. Minami, “Preparation of PbZrO3-PbTiO3 Ferroelectric Thin Films by the Sol-Gel Process,” Journal of the American Ceramic Society, vol. 74, no. 1, pp. 67–71, 1991.
[19] S. r. F. Jarner and E. Hansen, “Geometric ergodicity of Metropolis algorithms,” Stochastic Processes and their Applications,
vol. 85, no. 2, pp. 341–361, 2000. [Online]. Available: http://dx.doi.org/10.1016/S0304-4149(99)00082-4
[20] T. Janssen and J. A. Tjon, “One-dimensional model for a crystal with displacive modulation,” Phys. Rev. B, vol. 24, no. 4, pp. 2245–2248, 1981. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRevB.24.2245
[21] J.-M. Liu, W. M. Wang, Z. G. Liu, H. L. Chan, and C. L. Choy, “Dynamic hysteresis in ferroelectric systems: experiment and Monte Carlo simulation,” Applied Physics A, vol. 75, no. 4, pp. 507–514, 2002. [Online]. Available:
http://dx.doi.org/10.1007/s003390101012
[22] Y.-Z. Wu, D.-L. Yao, and Z.-Y. Li, “Monte-Carlo simulation of the switching behavior in ferroelectrics with dipolar defects,” Solid State Communications, vol. 122, no. 7-8, pp. 395–400, 2002.
[23] J. Hong and D. Fang, “Systematic study of the ferroelectric properties of Pb(Zr0.5Ti0.5)O3 nanowires,” Journal of Applied Physics, vol. 104, no. 6, pp. –, 2008. [Online]. Available: http://dx.doi.org/10.1063/1.2982090
[24] R. Yimnirun, Y. Laosiritaworn, and S. Wongsaenmai, “Effect of uniaxial compressive pre-stress on ferroelectric properties of soft PZT ceramics,” Journal of Physics D: Applied Physics, vol. 39, no. 4, p. 759, 2006. [Online]. Available: http://stacks.iop.org/0022-3727/39/i=4/a=025
[25] W. Smiga and B. Garbarz-Glos, “Studies of the influence of uniaxial pressure on the electric behaviour of Li0.015Na0.985NbO3 ceramics,” Ukrainian Journal of Physical Optics, vol. 13, no. 4, p. S27, 2012. [Online]. Available:
http://dx.doi.org/10.3116/16091833/13/1/s27/2012
[26] M. D. Nguyen, M. Dekkers, E. Houwman, R. Steenwelle, X. Wan, A. Roelofs, T. Schmitz-Kempen, and G. Rijnders, “Misfit strain dependence of ferroelectric and piezoelectric properties of clamped (001) epitaxial Pb(Zr0.52,Ti0.48)O3 thin films,” Applied Physics Letters, vol. 99, no. 25, pp. –, 2011. [Online]. Available: http://dx.doi.org/10.1063/1.3669527
[27] J. Suchanicz, N. T. H. Kim-Ngan, K. Konieczny, I. Jankowska-Sumara, D. Sitko, D. Goc-Jaglo, and A. G. Balogh, “Influence of combined external stress and electric field on electric properties of 0.5% Fe-doped lead zirconate titanate ceramics,” Journal of Applied Physics, vol. 106, no. 9, pp. 94 104–94 109, 2009. [Online]. Available: http://dx.doi.org/10.1063/1.3234394
[28] D. Guo, K. Cai, L. Li, and Z. Gui, “Investigation of the additive induced doping effects in gelcast soft lead zirconate titanate ceramics,” Journal of Applied Physics, vol. 106, no. 5, p. 054104, 2009. [Online]. Available: http://dx.doi.org/10.1063/1.3190549